Higher Spherical Scissors Congruence II: Comodules

We define the higher Dehn invariant on the Euclidean, hyperbolic, and spherical variants of scissors congruence $K$-theory, and prove that it makes these spectra into comodules over the spectral Sah algebra. This allows us to make the first formulation of the conjecture that the higher volume and Dehn invariants are jointly injective.

Authors

Cary Malkiewich (ORCID: https://orcid.org/0000-0002-4412-3622)
Josefien Kuijper (ORCID: https://orcid.org/0000-0002-9252-6645)
David Mehrle (ORCID: https://orcid.org/0000-0001-9186-7571)
Inbar Klang (ORCID: https://orcid.org/0000-0001-5019-6193)
Thor Wittich

Publication Details

Journal: arXiv (Cornell University)
Published: 2026-10-26
DOI: https://doi.org/10.48550/arxiv.2610.35567
Primary Topic: Homotopy and Cohomology in Algebraic Topology
Type: preprint

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preprint

Higher Spherical Scissors Congruence II: Comodules

Cary Malkiewich, Josefien Kuijper, David Mehrle, Inbar Klang et al.

Oct 26, 2026

arXiv (Cornell University)

Homotopy and Cohomology in Algebraic Topology

preprint

Higher Spherical Scissors Congruence II: Comodules

Cary Malkiewich, Josefien Kuijper, David Mehrle, Inbar Klang, Thor Wittich

October 26, 2026preprint en

Abstract

We define the higher Dehn invariant on the Euclidean, hyperbolic, and spherical variants of scissors congruence $K$-theory, and prove that it makes these spectra into comodules over the spectral Sah algebra. This allows us to make the first formulation of the conjecture that the higher volume and Dehn invariants are jointly injective.

arXiv (Cornell University)

Homotopy and Cohomology in Algebraic Topology

DOI Open Access PDF OpenAlex

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Higher Spherical Scissors Congruence II: Comodules — Cary Malkiewich, Josefien Kuijper, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS