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arXiv · 2501.06928

Scissors congruence K-theory for equivariant manifolds

Mona Merling·Ming Ng·Julia Semikina·Alba Sendón Blanco·Lucas Williams
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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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Mona Merling, Ming Ng, Julia Semikina, Alba Sendón Blanco, Lucas Williams. 2025-01-12. Scissors congruence K-theory for equivariant manifolds. https://arxiv.org/abs/2501.06928

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