---
- 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

## Meta

- **URL**: <https://arxiv.org/abs/1410.7120v3>
- **URI**: <http://zotero.org/users/1049732/items/7VY4QSK3>
- **Local File**: [Full Text PDF](file:///home/zack/Zotero/storage/9XXINJAF/Goodwillie%20-%202014%20-%20Scissors%20Congruence%20with%20Mixed%20Dimensions.pdf)
- **Open in Zotero**: [Zotero](zotero://select/library/items/7VY4QSK3)

## 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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