Algebraic & Geometric Topology

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

Markus Banagl and Greg Friedman

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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.

Article information

Source
Algebr. Geom. Topol., Volume 4, Number 1 (2004), 521-542.

Dates
Received: 10 May 2004
Accepted: 29 June 2004
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882486

Digital Object Identifier
doi:10.2140/agt.2004.4.521

Mathematical Reviews number (MathSciNet)
MR2077675

Zentralblatt MATH identifier
1067.57019

Subjects
Primary: 57Q15: Triangulating manifolds 57Q25: Comparison of PL-structures: classification, Hauptvermutung
Secondary: 57N80: Stratifications 57M27: Invariants of knots and 3-manifolds

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

Citation

Banagl, Markus; Friedman, Greg. Triangulations of 3–dimensional pseudomanifolds with an application to state-sum invariants. Algebr. Geom. Topol. 4 (2004), no. 1, 521--542. doi:10.2140/agt.2004.4.521. https://projecteuclid.org/euclid.agt/1513882486


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