Preprints:

• BNS invariants and algebraic fibrations of group extensions (with Stefano Vidussi)
  16 pages. Version 12/19.
• A survey of the foundations of four-manifold theory in the topological category (with Matthias Nagel, Patrick Orson and Mark Powell)
  100 pages. Version 10/19.
• Connected sum decompositions of high-dimensional manifolds (with Imre Bokor, Diarmuid Crowley, Fabian Hebestreit, Daniel Kasprowski, Markus Land and Johnny Nicholson)
  23 pages. Version 09/19.
• Graphical neighborhoods of spatial graphs (with Gerrit Herrmann)
  19 pages. Version 03/2020.
• The leading coefficient of the L^2-Alexander torsion (with Fathi Ben Aribi and Gerrit Herrmann)
  31 pages. Version 6/2018.
• Torsion in the homology of finite covers of 3-manifolds (with Gerrit Herrmann)
  9 pages. Version 10/2017.

Papers accepted for publication:

• Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials (with Lukas Lewark, Matthias Nagel, Mark Powell and Takahiro Kitayama)
  30 pages. Version 08/20.
  To be published by the Canadian Journal of Mathematics.
• Epimorphism testing with virtually Abelian targets (with Clara Löh), 18 pages.
  To be published by Confluentes Mathematici.
• On distinct finite covers of 3-manifolds (with JungHwan Park, Bram Petri, Jean Raimbault and Arunima Ray)
  26 pages. Version 08/18.
  To be published by the Indiana University Mathematics Journal
• Virtual algebraic fibrations of Kähler groups (with Stefano Vidussi)
  22 pages. Version 04/2017. to be published by the Nagoya Mathematical Journal
• Spatial graphs (with Gerrit Herrmann)
  to appear in the Encyclopedia of Knot Theory

Paper accepted for publication but which (alas!) never appeared in print.

• On the uniqueness of prime, Jacobi functors (with mathgen), 16 pages.
  The full story of this paper can be accessed at this blog.

Publications:

• Homotopy ribbon concordance and Alexander polynomials (with Mark Powell)
  Arch. Math. 115, No. 6, 717-725 (2020).
• Two-generator one-relator groups and marked polytopes (with Stephan Tillmann)
  Ann. Inst. Fourier 70, No. 2, 831-879 (2020).
• The profinite completion of 3-manifolds groups, fiberedness and the Thurston norm (with Michel Boileau)
  What’s next? The mathematical legacy of William P. Thurston. Annals of Mathematics Studies 205, 21-44 (2020).
• Grothendieck rigidity of 3-manifold groups (with Michel Boileau)
  Groups, Geometry & Dynamics 13 (2019), no. 4, 1133-1150.
• Groups and polytopes (with Wolfgang Lück and Stephan Tillmann)
  Breadth in contemporary topology, 57--77, Proc. Sympos. Pure Math., 102, Amer. Math. Soc., Providence, RI, 2019.
• Integral approximation of simplicial volume of graph manifolds (with Daniel Fauser and Clara Löh)
  Bulletin of the London Mathematical Society 51 (2019), no. 4, 715-731.
• The virtual Thurston seminorm of 3-manifolds (with Michel Boileau)
  Osaka Journal of Mathematics 56 (2019), no. 1, 51-63.
• L^2-Euler characteristics and the Thurston norm (with Wolfgang Lück)
  42 pages. Version 09/16. Proceedings of the London Mathematical Society 118 (2019), no. 4, 857-900.
• The L^2-torsion function and the Thurston norm of 3-manifolds (with Wolfgang Lück)
  22 pages. To be published by Commentarii Mathematici Helvetici 94 (2019), no. 1, 21-52.
• The Blanchfield pairing of colored links (with Anthony Conway and Enrico Toffoli)
  Indiana University Mathematics Journal 67, No. 6 (2018), 2151-2180.
• Satellites and concordance of knots in 3--manifolds (with Matthias Nagel, Patrick Orson and Mark Powell)
  Transactions of the American Mathematical Society 371, No. 4 (2019), 2279-2306.
• Linear representations of 3-manifold groups over rings (with Montek Gill and Stephan Tillmann)
  Proceedings of the American Mathematical Society 146 (2018), 4951-4966.
• Epimorphisms of 3-manifold groups (with Michel Boileau)
  The Quarterly Journal of Mathematics (2018), 931-942.
• Representation varieties detect essential surfaces (with Takahiro Kitayama and Matthias Nagel)
  Mathematical Research Letters 25 (2018), 803-817.
• Linking forms revisited (with Anthony Conway and Gerrit Herrmann)
  Pure and Applied Mathematics Quarterly 12 (2016), 493-515.
• On high-dimensional representations of knot groups (with Michael Heusener)
  Algebraic & Geometric Topology 18-1 (2018), 313-332.
• Twisted Blanchfield pairings and decomposition of 3-manifolds (with Constance Leidy, Matthias Nagel and Mark Powell)
  Homology, Homotopy and Applications 19 (2017), 275-287.
• An elementary proof of the group law for elliptic curves
  Groups, Complexity, Cryptology 9 (2017), no. 2, 117–123.
• Universal L^2-torsion, polytopes and applications to 3-manifolds (with Wolfgang Lück)
  Proceedings of the London Mathematical Society 114 (2017), 1114-1151.
• Thurston norm via Fox calculus (with Kevin Schreve and Stephan Tillmann)
  Geometry and Topology 21 (2017), 3759-3784.
• Splitting numbers of link (with Jae Choon Cha and Mark Powell)
  Proceedings of the Edinburgh Mathematical Society 60 (2017), 587–614
• Twisted Reidemeister torsion and the Thurston norm: graph manifolds and finite representations (with Matthias Nagel)
  Illinois Journal of Mathematics 59 (2015), 691-705.
• Knot concordances and alternating knots (with Chuck Livingston and Raphael Zentner)
  Michigan Math Journal 66 (2017), 421–432.
• Twisted Novikov homology of complex hypersurface complements (with Laurentiu Maxim)
  Mathematische Nachrichten 290 (2017), 604-612.
• Twisted Alexander invariants detect trivial links (with Stefano Vidussi)
  Canadian Mathematical Bulletin 60 (2017), 283-299.
• A note on the existence of essential tribranched surfaces (with Takahiro Kitayama and Matthias Nagel)
  Topology and its Applications 225 (2017) 75-82.
• A calculation of Blanchfield pairings of 3-manifolds and knots (with Mark Powell)
  Moscow Mathematical Journal 17 (2017), 59-77.
• The Grothendieck group of polytopes and norms (with Jae Choon Cha and Florian Funke)
  Münster Journal of Mathematics 10 (2017), 75-81.
• Novikov homology and noncommutative Alexander polynomials
  Journal of Knot Theory and its Ramifications 26, 1740013 (2017)
  Memorial volume for Tim Cochran of the Journal of Knot Theory and its Ramifications
• Rank gradients of infinite cyclic covers of Kahler manifolds (with Stefano Vidussi)
  Journal of Group Theory 19 (2016), 941-957.
• The L^2-Alexander torsion of 3-manifolds (with Jerome Dubois and Wolfgang Lück)
  Journal of Topology 9, No. 3 (2016), 889-926.
• The membership problem for 3-manifold groups is solvable (with Henry Wilton)
  Algebraic and Geometric Topology 16 (2016), 1827-1850.
• The Turaev and Thurston norms (with Daniel Silver and Susan Williams)
  Pacific Journal of Mathematics 284 (2016), 365-382.
• Blanchfield forms and Gordian distance (with Maciej Borodzik and Mark Powell)
  Journal of the Mathematical Society of Japan 68 (2016), no. 3, 1047–1080.
  Here is a slightly revised version which fixes a minor problem.
• Sutured Floer homology, fibrations, and taut depth one foliations (with Irida Altman and Andras Juhasz)
  Transactions of the American Mathematical Society 368, No. 9 (2016), 6363-6389.
• Twist spinning of knots and metabolizers of Blanchfield pairings (with Patrick Orson)
  Annales de la Faculte des Sciences de Toulouse 24 (2015), no. 5, 1203-1218.
• Decision problems for 3-manifolds and their fundamental groups (with Matthias Aschenbrenner and Henry Wilton)
  Baykur, R. Inanc (ed.) et al., Interactions between low dimensional topology and mapping class groups. Proceedings of the conference, Bonn, Germany, July 1-5, 2013. Geometry and Topology Monographs 19, 201-236 (2015).
• 3-manifolds that can be made acyclic (with Matthias Nagel)
  International Mathematics Research Notices 2015, no. 24, 13360-13378.
• The L^2-Alexander torsion is symmetric (with Jerome Dubois and Wolfgang Lück)
  Algebraic and Geometric Topology 15-6 (2015), 3599-3612.
• The Thurston norm and twisted Alexander polynomials (with Stefano Vidussi)
  Journal für Reine und Angewandte Mathematik 707 (2015), 87-102.
• 3-manifold groups (with Matthias Aschenbrenner and Henry Wilton)
  EMS Series of Lectures in Mathematics (2015), 230 pages. Preliminary version from 03/15.
• Virtually symplectic fibered 4-manifolds (with Inanc Baykur)
  Indiana University Mathematics Journal 64 No. 4 (2015), 983-999.
• Splittings of knot groups (with Daniel Silver and Susan Williams)
  Mathematische Annalen 362 (2015), 401-424.
• Three flavors of twisted invariants of knots (with Jerome Dubois and Wolfgang Lück)
  Introduction to Modern Mathematics, Advanced Lectures in Mathematics 33 (2015), 143-170.
• Thompson's Group F is not SCY (with Stefano Vidussi)
  Groups, Geometry and Dynamics 9 (2015), 325-329.
• The unknotting number and classical invariants I (with Maciej Borodzik)
  Algebraic and Geometric Topology 15 (2015), 85-135.
• On the algebraic unknotting number (with Maciej Borodzik)
  Transactions of the London Mathematical Society 1 (2014), 57-84.
• L^2-Alexander torsions of 3-manifolds (with Jerome Dubois and Wolfgang Lück)
  Comptes Rendus Mathematique 353 (2015), 69-73.
• Thurston's vision and the virtual fibering theorem for 3-manifolds
  Jahresbericht der Deutschen Mathematiker-Vereinigung 116 (2014), 223-241.
• A specious unlinking strategy (with Matthias Nagel and Mark Powell)
  Periodica Mathematica Hungarica 69 (2014), 207-210.
• Metabelian SL(n,C) representations of knot groups, III: deformations, (with Hans Boden)
  Quarterly Journal of Mathematics 65 (2014), 817-840.
• The virtual fibering theorem for 3-manifolds (with Takahiro Kitayama)
  L'enseignement mathematique 60 (2014), 79-107.
• Twisted Reidemeister torsion, the Thurston norm and fibered manifolds
  Geometriae Dedicata 172, (2014), 135-145.
• The unknotting number and classical invariants II (with Maciej Borodzik)
  Glasgow Mathematical Journal 56 (2014), 657-680.
• Concordance of links with identical Alexander invariants (with Jae Choon Cha and Mark Powell)
  Bulletin of the London Mathematical Society 46, No. 3 (2014), 629-642.
• Links Not Concordant to the Hopf Link (with Mark Powell)
  Math. Proc. Cambridge Philos. Soc. 156 (2014), no. 3, 425-459.
• A note on a topological approach to the mu-constant problem in dimension 2 (with Maciej Borodzik)
  Revista Matematica Complutense 27 (2014), 345-350.
• A Vanishing Theorem for Twisted Alexander Polynomials with Applications to Symplectic 4-manifolds (with Stefano Vidussi)
  Journal of the European Mathematical Society 15 (2013), no. 6, 2127-2041.
• Kaehler groups, quasi-projective groups, and 3-manifold groups (with Alexander Suciu)
  Journal of the London Mathematical Sociecty 89 (2014), 151-168.
• Rank gradients of infinite cyclic covers of 3-manifolds (with Jason Deblois and Stefano Vidussi)
  Michigan Journal of Mathematics 63 (2014), 65-81.
• Minimal Genus in 4-manifolds with a Free Circle Action (with Stefano Vidussi)
  Advances in Mathematics 250 (2014), 570-587.
• A note on the growth of Betti numbers and ranks of 3-manifold groups
  Bulletin des Sciences Mathematiques 138 (2014), 63-70.
• Metabelian SL(n,C) representations of knot groups IV: Twisted Alexander polynomials (with Hans Boden)
  Mathematical Proceedings of the Cambridge Philosophical Society 156 (2014), 81-97.
• Cobordisms to weakly splittable links (with Mark Powell)
  Proc. Amer. Math. Soc. 142 (2014), 703-712.
• On the topology of Symplectic Calabi-Yau 4-manifolds (with Stefano Vidussi)
  Journal of Topology (2013), 6 (4): 945-954.
• Taut sutured manifolds and twisted homology (with Taehee Kim)
  Mathematical Research Letter 20 (2013), no. 02, 1-15.
  Here's an erratum
• Commensurability of knots and L^2 invariants
  Proceedings of Geometry and Topology Down Under: The Rubinstein birthday conference. Contemporary Mathematics 597 (2013), 263-279.
• 3-manifold groups are virtually residually p (with Matthias Aschenbrenner)
  Memoirs Amer. Math. Soc. Vol 225 (2013), 106 pages.
• Twisted torsion invariants and link concordance (with Jae Choon Cha)
  Forum Mathematicum 25 (2013), 471-504.
• Poincare duality and degrees of twisted Alexander polynomials (with Taehee Kim and Takahiro Kitayama)
  Indiana University Mathematics Journal 61 (2012), 147-192.
• Twisted Alexander polynomials of hyperbolic knots (with Nathan Dunfield and Nicholas Jackson)
  Experimental Mathematics 21 (2012), 329-352.
  the program written by Nathan Dunfield and the full data can be found on Nathan's webpage
• Cosmetic crossings and Seifert matrices (with Cheryl Balm, Efstratia Kalfagianni and Mark Powell)
  Communications in Analysis and Geometry 20 (2012), 235-253.
• Construction of symplectic structures on 4-manifolds with a free circle action (with Stefano Vidussi)
  Proc. Royal Soc. Edinburgh: Section A 142 (2012), pp 359 - 370.
• An Injectivity Theorem for Casson-Gordon Type Representations relating to the Concordance of Knots and Links (with Mark Powell)
  Bull. Korean Math. Soc. 49 (2012), No. 2, 395-409
• Twisted Alexander polynomials and fibered 3-manifolds (with Stefano Vidussi)
  Low-Dimensional and Symplectic Topology, Proceedings of Symposia in Pure Mathematics Volume 82 (2011), 111-130.
• The decategorification of sutured Floer homology (with Andras Juhasz and Jacob Rasmussen)
  Journal of Topology (2011) 4(2): 431-478
• The cobordism group of homology cylinders (with Jae Choon Cha and Taehee Kim)
  Compositio Mathematica 147 (2011), 914-942
• Symplectic 4-manifolds with K=0 and the Lubotzky alternative (with Stefano Vidussi)
  Mathematics Research Letters 18 (2011) 513-519
• Residual properties of graph manifold groups (with Matthias Aschenbrenner)
  Topology and its Applications 158 (2011) 1179-1191
• Twisted Alexander polynomials detect fibered 3-manifolds (with Stefano Vidussi)
  Annals of Mathematics, Volume 173 (2011), 1587-1643
• A criterion for HNN extensions of finite p-groups to be residually p (with Matthias Aschenbrenner)
  Journal of Pure and Applied Algebra 215 (2011), 2280-2289.
• Metabelian SL(n,C) representations of knot groups II: fixed points (with Hans Boden)
  Pacific Journal of Mathematics, 249 (2011), 1-10
• A survey of twisted Alexander polynomials (with Stefano Vidussi)
  The Mathematics of Knots: Theory and Application (Contributions in Mathematical and Computational Sciences), editors: Markus Banagl and Denis Vogel (2010), p. 45-94.
• Realizations of Seifert matrices by hyperbolic knots
  J. Knot Theory and its Ramifications Volume 18 (2009), 1471-1474
• L^2-Betti numbers of plane algebraic curves (with Constance Leidy and Laurentiu Maxim)
  Michigan Math. Journal, 58 (2009), no. 2, 291-301
• New constructions of slice links (with Tim Cochran and Peter Teichner)
  Comment. Math. Helv. Volume 84, Issue 3 (2009), 617-638
• Twisted Alexander polynomials, symplectic 4-manifolds and surfaces of minimal complexity (with Stefano Vidussi)
  Banach Center Publ. 85 (2009), 43-57
  
• Metabelian SL(n,C) representations of knot groups (with Hans Boden)
  Pac. J. Math, Vol. 238, 7-25 (2008)
• Twisted Alexander norms give lower bounds on the Thurston norm (with Taehee Kim)
  Trans. Amer. Math. Soc. 360 (2008), 4597-4618
• Twisted Alexander polynomials and symplectic structures (with Stefano Vidussi)
  Amer. J. Math. 130, 455-484 (2008)
• The parity of the Cochran-Harvey invariants of 3-manifolds (with Taehee Kim)
  Trans. Amer. Math. Soc. 360 (2008), 2909-2922.
• Symplectic S^1 x N^3, surface subgroup separability, and totally degenerate Thurston norm (with Stefano Vidussi)
  Journal Amer. Math. Soc. 21 (2008), 597-610.
• Nontrivial Alexander polynomials of knots and links (with Stefano Vidussi)
  Bull. London Math. Soc., Vol. 39: 614-622 (2007)
• Non-smoothable four-manifolds with cyclic fundamental group (with Ian Hambleton, Paul Melvin, Peter Teichner)
  Inter. Math. Res. Not., Vol. 2007, Article ID rnm031, 20 pages
• Reidemeister torsion, the Thurston norm and Harvey's invariants
  Pacific Journal of Mathematics, Vol. 230: 271-296 (2007)
• Non-commutative Multivariable Reidemeister Torsion and the Thurston Norm (with Shelly Harvey)
  Alg. Geom. Top., Vol. 7: 755-777 (2007)
• Algorithm for finding boundary link Seifert matrices
  Journal of Knot Theory and its Ramifications, Vol 15, No. 5: 601-612 (2006)
• The Thurston norm, fibered manifolds and twisted Alexander polynomials (with Taehee Kim)
  Topology 45: 929-953 (2006)
• New topologically slice knots (with Peter Teichner)
  Geometry and Topology, Volume 9 (2005) Paper no. 48, pages 2129-2158
  and the correction to an example
  Correction to New topologically slice knots
  Geometry and Topology, Volume 10 (2006), 3001-3004. and another erratum
• Full signature invariants for L_0(F(t))
  Proc. Amer. Math. Soc. 133: 647-653 (2005)
• L^2-eta-invariants and their approximation by unitary eta-invariants
  Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 138: 327-338 (2005)
• Link concordance, boundary link concordance and eta-invariants
  Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 138: 437-460 (2005)
• Eta invariants as sliceness obstructions and their relation to Casson-Gordon invariants
  Algebraic and Geometric Topology, Vol. 4: 893-934 (2004)

Papers in non-refereed publications:

• Symplectic S^1 x N^3 and subgroup separability (with Stefano Vidussi)
  Oberwolfach Reports, Volume 3, Issue 3 (2006), 2166 - 2168
• Fundamental groups of 3-manifolds (on joint work with Matthias Aschenbrenner)
  Oberwolfach Reports, Volume 7, Issue 3 (2010), 2479-2482
• Centralizers in 3-manifold groups
  RIMS Kokyuroku 1747 (2011), 23-34
• Approximations to the hyperbolic volume of knots (with Nicholas Jackson)
  13 pages, RIMS Kokyuroku 1747 (2011), 35-46
• Cobordism on homology cylinders and combinatorial torsions (with Jae Choon Cha and Taehee Kim)
  RIMS Kokyuroku 1747 (2011), 17-22
• The Thurston norm via Fox calculus (with Kevin Schreve and Stephan Tillmann)
  Oberwolfach reports 12 (2015), 200-202.
• Profinite completions and 3-manifold groups (with Michel Boileau)
  RIMS Kokyuroku (2016), 15 pages.

Lecture notes:

• Lecture notes for Analysis I: Koeln 2010-2011 (123 Seiten) und Regensburg 2014-2015 (200 Seiten)
• Lecture notes for Analysis II, (127 Seiten)
• Lecture notes for Analysis III, (169 Seiten)
• Lecture notes for Topologie, (163 Seiten)
• Lecture notes for Algebraische Topologie, (169 Seiten)
• Lecture notes for Hyperbolische Geometrie, (122 Seiten)
• Lecture notes for algebraic torsion, (29 pages)
• An introduction to 3-manifolds
  28 pages, lectures held at a summer school in Muenster, Germany, July 18-21 2011
  and an expanded version of the above with 37 pages

Videos from talks

• Symplectic 4-manifolds of the form S^1xN, Chern Centennial Conference, November 2011, MSRi
• The algebraic unknotting number, University of Edinburgh, February 2012.
• Minimal genus surfaces in 4-manifolds with a free S^1-action, KAIST, August 2012.
• Topologically slice knots, University of Edinburgh, July 2013.
• Splittings of knot groups, Geometric Topology in New York, August 2013.
• Slicing knots, BIRS, Banff, February 2016.

Talks for a general audience:

• The possible shapes of the universe and the virtual fibering theorem, Keble College, February 2014.

Slides and talks:

• Knots, graphs, surfaces in dimensions 3 and 4, CIRM Luminy, February 2017.
• Complexity of surfaces in 4-manifolds with a free circle action, University of Akron, October 2012
• The algebraic unknotting number, University of Edinburgh, February 2012 et aussi le nombre de denouage algebrique a Paris VII Mars 2012
• Minimal genus Seifert surfaces are robust, University of Warwick, February 2012.
• A survey of twisted Alexander polynomials, Akita, September 2010.
• Twisted Alexander, fibered 3-manifolds and the Thurston norm, Akita, September 2010.
• Twisted Alexander polynomials of hyperbolic knots, AMS-KMS joint conference, Seoul, December 2009.
• Les varietes fibrees de dimension trois et les varietes symplectiques de dimension quatre, Conference a Paris VII, Mai 2009.
• Symplectic 4-manifolds and fibered 3-manifolds, talk at the 5th East Asian conference on knots, January 2009.
• Symplectic 4-manifolds and fibered 3-manifolds, talk at Brandeis University, June 2008
• New examples of topologically slice knots and links, talk at the University of Waterloo, November 2007
• Symplectic 4-manifolds and fibered 3-manifolds, talk at the Low Dimensional Geometry and Topology Symposium at Warwick 2007
• 4-manifolds and their (equivariant) intersection forms, talk at University of California at Riverside 2007
• Commensurabiliy and L^2-invariants, talk at Columbia University 2007
• Twisted Alexander polynomials and Symplectic Structures, talk in Baton Rouge 2006 on joint work with Stefano Vidussi
• Twisted Alexander polynomials, the Thurston norm and symplectic manifolds, talk at UC-Berkeley 2005 on joint work with Taehee Kim and Stefano Vidussi
• Examples of topologically slice knots, talk in Edinburgh 2005 on joint work with Peter Teichner

Miscellaneous notes:

• Primzahltests und Faktorisierungsmethoden, Zulassungsarbeit fuer das Staatsexamen fuer Lehramt Gymnasium, Regensburg (1997)
• Eta invariants as sliceness obstructions and their relation to Casson-Gordon invariants , PhD thesis, Brandeis University (2003), see also the erratum to Corollary 9.3
• Symplectic 4-manifolds with a free circle action (with Stefano Vidussi)
  this paper was split into several papers, parts of it appear in 'Construction of symplectic structures on 4-manifolds with a free circle action' and in `Symplectic 4-manifolds with K=0 and the Lubotzky alternative'
• The Thurston norm, fibered manifolds and twisted Alexander polynomials (more detailed version of the above paper with 51 pages)
• Alexander polynomials of plane algebraic curves, 21 pages. A note slightly generalizing results of Cogolludo-Florens and Leidy-Maxim (2005)
• Hyperbolic examples of topologically slice knots, 5 pages (2007)
• Notes taken at a talk by Dani Wise on `The structure of groups with a quasi-convex hierarchy' in Montreal, 21 pages (April 2010)
• Concordance of links and their components, 2 pages (April 2011)
• 3-manifolds after Perelman, 12 pages, extended version of a talk given at the Max-Planck institute in Bonn (October 2011)
• A quick proof that K #-K is doubly slice (with Patrick Orson), 6 pages (December 2013)
• Cyclic resultants of reciprocal polynomials, an exposition of the eponymous paper of David Fried, talk given July 2015.
• Linking forms of amphichiral knots (with Allison Miller and Mark Powell) 7 pages (2017)
• The Picard Theorem 14 pages (2017)