Volume 4, issue 1 (2004)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Triangulations of 3–dimensional pseudomanifolds with an application to state-sum invariants

Markus Banagl and Greg Friedman

Algebraic & Geometric Topology 4 (2004) 521–542

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