Raptis, George and Steimle, Wolfgang (2020) TOPOLOGICAL MANIFOLD BUNDLES AND THE A-THEORY ASSEMBLY MAP. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 148 (9). pp. 3787-3799. ISSN 0002-9939, 1088-6826
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We give a new proof of an index theorem for fiber bundles of compact topological manifolds due to Dwyer, Weiss, and Williams, which asserts that the parametrized A-theory characteristic of such a fiber bundle factors canonically through the assembly map of A-theory. Furthermore our main result shows a refinement of this statement by providing such a factorization for an extended A-theory characteristic, defined on the parametrized topological cobordism category. The proof uses a convenient framework for bivariant theories and recent results of Gomez-Lopez and Kupers on the homotopy type of the topological cobordism category. We conjecture that this lift of the extended A-theory characteristic becomes highly connected as the manifold dimension increases.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ALGEBRAIC K-THEORY; COBORDISM CATEGORY; MODEL; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Ulrich Bunke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 17 Mar 2021 09:48 |
| Last Modified: | 17 Mar 2021 09:48 |
| URI: | https://pred.uni-regensburg.de/id/eprint/43959 |
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