Dehn-Sydler-Jessen Via Homological Algebra

TL;DR

This paper introduces a homological algebra approach to Euclidean scissors congruence, providing an expository review of the Dehn-Sydler-Jessen Theorem and its proof.

Contribution

It re-frames scissors congruence problems in terms of group homology, offering a new perspective and simplifying the understanding of the Dehn-Sydler-Jessen Theorem.

Findings

Reformulation of scissors congruence in homological terms

Clear exposition of the Dehn-Sydler-Jessen Theorem proof

Bridging geometric and algebraic approaches in polytope theory

Abstract

We provide an expository introduction to Euclidean Scissors Congruence, the study of polytopes in Euclidean space up to `cut and paste' relations. We first re-frame questions in scissors congruence as those in group homology. We then use this perspective to review the proof of the Dehn-Sydler-Jessen Theorem as found in the works of Dupont and Sah.