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PreprintCC BY-NC-ND 4.0arXiv

Higher Spherical Scissors Congruence II: Comodules

  • Inbar Klang
  • Josefien Kuijper
  • Cary Malkiewich
  • David Mehrle
  • Thor Wittich
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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.

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Cite

BibTeXRIS
BibTeX
@misc{klang2026higher,
  title = {{Higher Spherical Scissors Congruence II: Comodules}},
  author = {Inbar Klang and Josefien Kuijper and Cary Malkiewich and David Mehrle and Thor Wittich},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35567},
  eprint = {2610.35567},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35567},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Higher Spherical Scissors Congruence II: Comodules
AU  - Inbar Klang
AU  - Josefien Kuijper
AU  - Cary Malkiewich
AU  - David Mehrle
AU  - Thor Wittich
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35567
UR  - https://arxiv.org/abs/2610.35567
AB  - 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.
ER  -