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 -theory of .
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