All K-theory is squares K-theory

2025/12/01 by Josefien Kuijper, Kuijper, Josefien · 3 voices
#math.KT #math.AT

paper · pdf · doi:10.48550/arxiv.2512.01813

Abstract

We show that the K-theory spectra of many assemblers, such as the assembler of polytopes in euclidean, hyperbolic or spherical geometry, as well as the assembler of definable sets, are equivalent to the K-theory spectrum of a squares category. We use this to lift the definable Euler characteristic of definable sets in an o-minimal structure to a map of K-theory spectra.

Citations

• Higher Spherical Scissors Congruence I: Hopf Algebra
• Scissors congruence K-theory for equivariant manifolds
• A trace map on higher scissors congruence groups
• Devissage and Localization for the Grothendieck Spectrum of Varieties
• Geometric realization and its variants
• Homotopy theory of simplicial presheaves in completely decomposable topologies

Discussions

• Is this the first time Huey Lewis and the News have appeared in a mathematics paper? arxiv.org/abs/2512.01813 [bsky, 10 points, 3 comments]
• Josefien Kuijper All K-theory is squares K-theory https://arxiv.org/abs/2512.01813 [bsky, 0 points, 0 comments]
• Josefien Kuijper: All K-theory is squares K-theory https://arxiv.org/abs/2512.01813 https://arxiv.org/pdf/2512.01813 https://arxiv.org/html/2512.01813 [bsky, 0 points, 0 comments]

Related

• Algebraic K-theory for squares categories
• The K-theory of assemblers
• KK-theory of C*-categories and the analytic assembly map
• Polytopes and K-theory
• Algebraic K-theory Spectra and Factorisations of Analytic Assembly Maps