Algebraic & Geometric Topology

Coverings and minimal triangulations of $3$–manifolds

William Jaco, J Hyam Rubinstein, and Stephan Tillmann

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This paper uses results on the classification of minimal triangulations of 3–manifolds to produce additional results, using covering spaces. Using previous work on minimal triangulations of lens spaces, it is shown that the lens space L(4k,2k1) and the generalised quaternionic space S3Q4k have complexity k, where k2. Moreover, it is shown that their minimal triangulations are unique.

Article information

Algebr. Geom. Topol., Volume 11, Number 3 (2011), 1257-1265.

Received: 28 February 2009
Revised: 27 June 2009
Accepted: 23 July 2009
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57N10: Topology of general 3-manifolds [See also 57Mxx]

$3$–manifold minimal triangulation layered triangulation efficient triangulation complexity prism manifold small Seifert fibred space


Jaco, William; Rubinstein, J Hyam; Tillmann, Stephan. Coverings and minimal triangulations of $3$–manifolds. Algebr. Geom. Topol. 11 (2011), no. 3, 1257--1265. doi:10.2140/agt.2011.11.1257.

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