Algebraic & Geometric Topology

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

Markus Banagl and Greg Friedman

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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