Scissors congruence K-theory for equivariant manifolds

2025/01/12 by Merling, Mona, Ng, Ming, Semikina, Julia +2 · 3 citations
#19A49 #19D99 #55P91 #55S91 #57R91 #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Primary: 19D55 #Secondary: 19D10

paper · doi:10.48550/arxiv.2501.06928

Abstract

We introduce a scissors congruence K-theory spectrum which lifts the equivariant scissors congruence groups for compact G-manifolds with boundary, and we show that on π₀ this is the source of a spectrum level lift of the Burnside ring valued equivariant Euler characteristic of a compact G-manifold. We also show that the equivariant scissors congruence groups for varying subgroups assemble into a Mackey functor, which is a shadow of a conjectural higher genuine equivariant structure.

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