English

Hilbert's third problem and a conjecture of Goncharov

K-Theory and Homology 2022-04-29 v8 Algebraic Geometry Algebraic Topology

Abstract

In this paper we reduce the generalized Hilbert's third problem about Dehn invariants and scissors congruence classes to the injectivity of certain Chern--Simons invariants. We also establish a version of a conjecture of Goncharov relating scissors congruence groups of polytopes and the algebraic KK-theory of C\mathbf{C}.

Keywords

Cite

@article{arxiv.1910.07112,
  title  = {Hilbert's third problem and a conjecture of Goncharov},
  author = {Jonathan Campbell and Inna Zakharevich},
  journal= {arXiv preprint arXiv:1910.07112},
  year   = {2022}
}

Comments

Current version is slightly different from previous: the maps relating K-theory and the Goncharov complex go in the other direction

R2 v1 2026-06-23T11:44:55.487Z