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2021 An additivity theorem for cobordism categories
Wolfgang Steimle
Algebr. Geom. Topol. 21(2): 601-646 (2021). DOI: 10.2140/agt.2021.21.601

Abstract

Using methods inspired from algebraic K–theory, we give a new proof of the Genauer fibration sequence, relating the cobordism categories of closed manifolds with cobordism categories of manifolds with boundaries, and of the Bökstedt–Madsen delooping of the cobordism category. Unlike the existing proofs, this approach generalizes to other cobordism-like categories of interest. Indeed we argue that the Genauer fibration sequence is an analogue, in the setting of cobordism categories, of Waldhausen’s additivity theorem in algebraic K–theory.

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Wolfgang Steimle. "An additivity theorem for cobordism categories." Algebr. Geom. Topol. 21 (2) 601 - 646, 2021. https://doi.org/10.2140/agt.2021.21.601

Information

Received: 20 February 2019; Revised: 20 April 2020; Accepted: 22 June 2020; Published: 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.2140/agt.2021.21.601

Subjects:
Primary: 57R90
Secondary: 19D06, 57R15, 57R56

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.21 • No. 2 • 2021
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