On the functoriality of the space of equivariant smooth h-cobordisms

2023/03/27 by Thomas G. Goodwillie, Goodwillie, Thomas, Kiyoshi Igusa +5 · 1 citation
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2303.14892

openalex publication_date 2023/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct an (∞,1)-functor that takes each smooth G-manifold with corners M to the space of equivariant smooth h-cobordisms \mathcal H_Diff(M). We also give a stable analogue \mathcal H^{\mathcal U}_Diff(M) where the manifolds are stabilized with respect to representation discs. The functor structure is subtle to construct, and relies on several new ideas. In the non-equivariant case G=e, our (∞,1)-functor agrees with previous constructions of the smooth h-cobordism space as a functor to the homotopy category.

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• Trace methods for equivariant algebraic K-theory

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