Scissors congruence K‐theory for equivariant manifolds
Abstract We introduce a scissors congruence ‐theory spectrum that 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.
Authors
- Julia Semikina (ORCID: https://orcid.org/0000-0001-8779-8518)
- Lucas Williams
- A. Blanco (ORCID: https://orcid.org/0000-0002-1921-221X)
- Ming Ng
- Mona Merling
Institutions
- Binghamton University (US)
- Laboratoire Paul Painlevé (FR)
- Nagoya University (JP)
- University of Pennsylvania (US)
- Vrije Universiteit Amsterdam (NL)
Publication Details
- Journal
- Bulletin of the London Mathematical Society
- Published
- 2025-09-04
- DOI
- https://doi.org/10.1112/blms.70181
- Primary Topic
- Homotopy and Cohomology in Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Agence Nationale de la Recherche
- Engineering and Physical Sciences Research Council
- Japan Society for the Promotion of Science
- Division of Mathematical Sciences