Raptis, George and Steimle, Wolfgang (2017) Parametrized cobordism categories and the Dwyer-Weiss-Williams index theorem. JOURNAL OF TOPOLOGY, 10 (3). pp. 700-719. ISSN 1753-8416, 1753-8424
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We define parametrized cobordism categories and study their formal properties as bivariant theories. Bivariant transformations to a strongly excisive bivariant theory give rise to characteristic classes of smooth bundles with strong additivity properties. In the case of cobordisms between manifolds with boundary, we prove that such a bivariant transformation is uniquely determined by its value at the universal disk bundle. This description of bivariant transformations yields a short proof of the Dwyer-Weiss-Williams family index theorem for the parametrized A-theory Euler characteristic of a smooth bundle.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ALGEBRAIC K-THEORY; MAP; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Ulrich Bunke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:15 |
| Last Modified: | 12 Feb 2019 15:16 |
| URI: | https://pred.uni-regensburg.de/id/eprint/1347 |
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