English

Scissors congruence K-theory for equivariant manifolds

Algebraic Topology 2025-08-18 v2 K-Theory and Homology

Abstract

We introduce a scissors congruence KK-theory spectrum which lifts the equivariant scissors congruence groups for compact GG-manifolds with boundary, and we show that on π0\pi_0 this is the source of a spectrum level lift of the Burnside ring valued equivariant Euler characteristic of a compact GG-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.

Keywords

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