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Register a new userHilberts third problem and a conjecture of Goncharov
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In this paper we reduce the generalized Hilberts 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 $mathbf{C}$.
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