- CiteKey: “Goo17” - Type: journalArticle - Title: “Scissors Congruence with Mixed Dimensions,” - Author: “Goodwillie, Thomas G.;” - Year: 2014 - DOI: 10.48550/arXiv.1410.7120 - Collections: “Syllabus; Talbot 2022,”
Scissors Congruence with Mixed Dimensions
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- URL: https://arxiv.org/abs/1410.7120v3
- URI: http://zotero.org/users/1049732/items/7VY4QSK3
- Open in Zotero: Zotero
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.