Algebraic and Geometric Topology 4 (2004), paper no. 24, pages 521-542.

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

Markus Banagl, Greg Friedman

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

AMS subject classification. Primary: 57Q15, 57Q25. Secondary: 57N80, 57M27.

DOI: 10.2140/agt.2004.4.521

E-print: arXiv:math.GT/0408156

Submitted: 10 May 2004. Accepted: 29 June 2004. Published: 11 July 2004.

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Markus Banagl, Greg Friedman
Mathematisches Institut, Universitat Heidelberg
D-69120 Heidelberg, Germany
Department of Mathematics, Yale University
New Haven, CT 06520, USA

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