Udo Pachner (1947-2002) - A "Hidden Champion" in Mathematics

TL;DR

Udo Pachner's work established that all homeomorphic simplicial manifolds can be related through finite types of local transformations, enabling the identification of invariants crucial for topology and quantum gravity.

Contribution

The paper highlights Pachner's foundational results on transformations of simplicial manifolds and their significance across topology and physics.

Findings

Finite types of Pachner moves for fixed dimensions

Invariance of topological properties under Pachner moves

Applications in topology and loop quantum gravity

Abstract

Udo Pachner proved that all simplicial manifolds which are homeomorphic can be transformed into each other by a sequence of simple transformations now commonly called "Pachner moves". For a fixed dimension there are only finitely many types of Pachner moves. This makes it possible to identify invariants by proving the invariance only for a finite number of transformations. This fact has proved useful for various applications in p.l. topology and in loop quantum gravity theory. The paper is meant to honor the importance of Pachner's results and to make them known to a wider community.