Work

Scissors congruence K‐theory for equivariant manifolds

Year: 2025

Type: article

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.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70181

Authors: Mona Merling, Ming Ng, Julia Semikina, Alba Sendón Blanco, Lucas Williams

Institutions: University of Pennsylvania, Nagoya University, Université de Lille, Laboratoire Paul Painlevé, Vrije Universiteit Amsterdam, Binghamton University

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: National Science Foundation, Vanderbilt University, Agence Nationale de la Recherche, Engineering and Physical Sciences Research Council, Japan Society for the Promotion of Science, Division of Mathematical Sciences

Awards: G1050467133, G1103661064, FRG: Collaborative Research: Trace Methods and Applications for Cut-and-Paste K-Theory, G3257718068, Model theoretic and topos theoretic view of difference algebra and applications to dynamics, Centre Européen pour les Mathématiques, la Physique et leurs Interactions, CAREER: Applications of equivariant homotopy theory to manifolds, G6068480032, G6671297155, G783409827, FRG: Collaborative Research: Trace Methods and Applications for Cut-and-Paste K-Theory

OpenAlex ID: W4413974326

FWCI: 1.604

Cites: 25

Cited by: 1

Related to: 10