The equivariant parametrized h-cobordism theorem, the non-manifold part

2020/01/15 by Cary Malkiewich, Malkiewich, Cary, Mona Merling +1 · 2 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2001.05563

Abstract

We construct a map from the suspension G-spectrum Σ_G^∞ M of a smooth compact G-manifold to the equivariant A-theory spectrum A_G(M), and we show that its fiber is, on fixed points, a wedge of stable h-cobordism spectra. This map is constructed as a map of spectral Mackey functors, which is compatible with tom Dieck style splitting formulas on fixed points. In order to synthesize different definitions of the suspension G-spectrum as a spectral Mackey functor, we present a new perspective on spectral Mackey functors, viewing them as multifunctors on indexing categories for "rings on many objects" and modules over such. This perspective should be of independent interest.

Cited by

• An isovariant Blakers--Massey theorem
• Segal K-theory factors through Waldhausen categories

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