DFG-Projekt AM 144/2-1
Small eigenvalues of the Dirac operator, Surgery and Bordism theory
Applicant
Bernd Ammann, Regensburg
Description
In the project we want to study several topics about small
eigenvalues of the Dirac operator and its connections to bordism theory.
- Bordism theory for manifolds without harmonic spinors:
Harmonic spinors are spinors to the eigenvalue 0.
This eigenvalue plays a very particular role, mainly due to its topological
significance from Atiyah-Singer index theory. We want to extend recent
progress on such questions in order to obtain a bordism theory for manifolds
without harmonic spinors.
- Equivariant harmonic L2-spinors:
We study harmonic L2-spinors
and Fredholmness of the Dirac operator on possibly non-compact coverings of
compact manifolds.
- Prescribing small eigenvalues of the Dirac operator using
surgery techniques.
- Yamabe-type invariants of conformally covariant operators and
its invariance under bordisms.
- Manifolds with boundaries.
- Relations to general relativity.
For all these subjects bordisms and surgeries play a central role
for proving the existence of metrics with certain properties.
Financed projects
- Postdoc position for Nadine Große
- PhD position for Andreas Hermann
Bernd Ammann, 8.8.8 or later