Scissors Congruence with Mixed Dimensions

2014/10/27 by Goodwillie, Thomas G.
#FOS: Mathematics #K-Theory and Homology (math.KT) #Primary: 52B45

paper · doi:10.48550/arxiv.1410.7120

Abstract

We introduce a Grothendieck group E_n for bounded polytopes in \mathbb Rⁿ. It differs from the usual Euclidean scissors congruence group in that lower-dimensional polytopes are not ignored. We also define an analogous group L_n using germs of polytopes at a point, which is related to spherical scissors congruence. This provides a setting for a generalization of the Dehn invariant.

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