Mapping the surgery exact sequence for topological manifolds to analysis
| Autor: | Vito Felice Zenobi |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
surgery theory
Mathematics - Differential Geometry Topology Dirac operator K-theory 01 natural sciences Mathematics - Geometric Topology symbols.namesake Mathematics::K-Theory and Homology 0103 physical sciences FOS: Mathematics coarse geometry 0101 mathematics Mathematics::Symplectic Geometry Mathematics 010102 general mathematics K-Theory and Homology (math.KT) Geometric Topology (math.GT) Surgery theory Lipschitz continuity Mathematics::Geometric Topology Differential Geometry (math.DG) Signature operator Surgery exact sequence Mathematics - K-Theory and Homology Lipschitz manifolds symbols Equivariant map 010307 mathematical physics Geometry and Topology Atiyah–Singer index theorem Analysis |
| Zdroj: | Journal of Topology and Analysis. :329-361 |
| ISSN: | 1793-7167 1793-5253 |
| DOI: | 10.1142/s179352531750011x |
| Popis: | In this paper we prove the existence of a natural mapping from the surgery exact sequence for topological manifolds to the analytic surgery exact sequence of N. Higson and J. Roe. This generalizes the fundamental result of Higson and Roe, but in the treatment given by Piazza and Schick, from smooth manifolds to topological manifolds. Crucial to our treatment is the Lipschitz signature operator of Teleman. We also give a generalization to the equivariant setting of the product defined by Siegel in his Ph.D. thesis. Geometric applications are given to stability results for rho classes. We also obtain a proof of the APS delocalised index theorem on odd dimensional manifolds, both for the spin Dirac operator and the signature operator, thus extending to odd dimensions the results of Piazza and Schick. Consequently, we are able to discuss the mapping of the surgery sequence in all dimensions. 26 pages, accepted in "Journal of Topology and Analysis" |
| Databáze: | OpenAIRE |
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