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arXiv · 2508.03621

A genuine $G$-spectrum for the cut-and-paste $K$-theory of $G$-manifolds

Maxine Calle·David Chan
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Abstract

Recent work has applied scissors congruence $K$-theory to study classical cut-and-paste ($SK$) invariants of manifolds. This paper proves the conjecture that the squares $K$-theory of equivariant $SK$-manifolds arises as the fixed points of a genuine $G$-spectrum. Our method utilizes the framework of spectral Mackey functors as models for genuine $G$-spectra, and our main technical result is a general procedure for constructing spectral Mackey functors using squares $K$-theory.

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Maxine Calle, David Chan. 2026-03-26. A genuine $G$-spectrum for the cut-and-paste $K$-theory of $G$-manifolds. https://doi.org/10.1112/blms.70352

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