Ammann, Bernd and Dahl, Mattias and Humbert, Emmanuel (2009) Surgery and the Spinorial tau-Invariant. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 34 (10): PII 915163. pp. 1147-1179. ISSN 0360-5302,
Full text not available from this repository. (Request a copy)Abstract
We associate to a compact spin manifold M a real-valued invariant (M) by taking the supremum over all conformal classes of the infimum inside each conformal class of the first positive Dirac eigenvalue, when the metrics are normalized to unit volume. This invariant is a spinorial analogue of Schoen's sigma-constant, also known as the smooth Yamabe invariant. We prove that if N is obtained from M by surgery of codimension at least 2 then (N) epsilon min{(M), n}, where n is a positive constant depending only on n=dim M. Various topological conclusions can be drawn, in particular that is a spin-bordism invariant below n. Also, below n the values of cannot accumulate from above when varied over all manifolds of dimension n.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DIRAC OPERATOR; HARMONIC SPINORS; EIGENVALUE; Dirac operator; Eigenvalue; Surgery |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Bernd Ammann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 12 Oct 2020 06:56 |
| Last Modified: | 12 Oct 2020 06:56 |
| URI: | https://pred.uni-regensburg.de/id/eprint/29696 |
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