Scissors congruence K-theory for equivariant manifolds
Algebraic Topology
2025-08-18 v2 K-Theory and Homology
Abstract
We introduce a scissors congruence -theory spectrum which lifts the equivariant scissors congruence groups for compact -manifolds with boundary, and we show that on this is the source of a spectrum level lift of the Burnside ring valued equivariant Euler characteristic of a compact -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.
Cite
@article{arxiv.2501.06928,
title = {Scissors congruence K-theory for equivariant manifolds},
author = {Mona Merling and Ming Ng and Julia Semikina and Alba Sendón Blanco and Lucas Williams},
journal= {arXiv preprint arXiv:2501.06928},
year = {2025}
}
Comments
Final version to appear in BLMS. We thank a very careful referee for many useful suggestions