Triangulations of 3–dimensional pseudomanifolds with an application to state-sum invariants

Banagl, Markus; Friedman, Greg

doi:10.2140/agt.2004.4.521

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Triangulations of 3–dimensional pseudomanifolds with an application to state-sum invariants

Markus Banagl and Greg Friedman

Algebraic & Geometric Topology 4 (2004) 521–542

DOI: 10.2140/agt.2004.4.521

arXiv: math.GT/0408156

Abstract

We demonstrate the triangulability of compact 3–dimensional topological pseudomanifolds and study the properties of such triangulations, including the Hauptvermutung and relations by Alexander star moves and Pachner bistellar moves. We also provide an application to state-sum invariants of 3–dimensional topological pseudomanifolds.

Keywords

pseudomanifold, triangulation, Hauptvermutung, Alexander star move, bistellar move, Pachner move, state-sum invariant, Turaev–Viro invariant, quantum invariant

Mathematical Subject Classification 2000

Primary: 57Q15, 57Q25

Secondary: 57N80, 57M27

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Publication

Received: 10 May 2004

Accepted: 29 June 2004

Published: 11 July 2004

Authors

Markus Banagl
Mathematisches Institut Universität Heidelberg D-69120 Heidelberg Germany

Greg Friedman
Department of Mathematics Yale University New Haven CT 06520 USA

Volume 4, issue 1 (2004)