Hilbert's third problem and a conjecture of Goncharov

2019/10/16 by Campbell, Jonathan, Zakharevich, Inna
#18G40 #19D55 #19E99 #19F27 #52B45 #55U10 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1910.07112

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 K-theory of C.

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