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arXiv · 1410.7120

Scissors Congruence with Mixed Dimensions

Thomas G. Goodwillie
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Abstract

We introduce a Grothendieck group $E_n$ for bounded polytopes in $\mathbb R^n$. 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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Thomas G. Goodwillie. 2014-10-27. Scissors Congruence with Mixed Dimensions. https://arxiv.org/abs/1410.7120

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