A linearization map for genuine equivariant algebraic K-theory

2023/09/14 by Calle, Maxine, Chan, David, Mejia, Andres · 3 citations
#19L47 (Secondary) #55P91 (Primary) 19D10 #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2309.08025

Abstract

We introduce a version of algebraic K-theory for coefficient systems of rings which is valued in genuine G-spectra for a finite group G. We use this construction to build a genuine G-spectrum K_G(ℤ[\underlineπ₁(X)]) associated to a G-space X, which provides a home for equivariant versions of classical invariants like the Wall finiteness obstruction and Whitehead torsion. We provide a comparison between our K-theory spectrum and the equivariant A-theory of Malkiewich--Merling via a genuine equivariant linearization map.

Cited by

• Derived induction theory for the K-theory of modular group algebras
• A genuine G-spectrum for the cut-and-paste K-theory of G-manifolds
• The spectrum of the Burnside Tambara functor

Related

• Equivariant algebraic K-theory of G-rings
• A kind of KK-theory for rings
• The Galois-equivariant K-theory of finite fields
• Equivariant Algebraic K-Theories
• Equivariant K-theory of finite dimensional real vector spaces