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Scissors congruence K-theory for equivariant manifolds

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arxiv 2501.06928 v2 pith:Q2EAG7ZR submitted 2025-01-12 math.AT math.KT

Mona Merling , Ming Ng , Julia Semikina , Alba Sendón Blanco , Lucas Williams This is my paper · ORCID
classification math.ATmath.KT
keywords equivariantcongruencescissorscompactgroupsmanifoldsspectrumassemble
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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 $\pi_0$ 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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