#### Volume 11, issue 3 (2011)

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Coverings and minimal triangulations of $3$–manifolds

### William Jaco, J Hyam Rubinstein and Stephan Tillmann

Algebraic & Geometric Topology 11 (2011) 1257–1265
##### Abstract

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 $L\left(4k,2k-1\right)$ and the generalised quaternionic space ${S}^{3}∕{Q}_{4k}$ have complexity $k$, where $k\ge 2$. Moreover, it is shown that their minimal triangulations are unique.

##### Keywords
$3$–manifold, minimal triangulation, layered triangulation, efficient triangulation, complexity, prism manifold, small Seifert fibred space
##### Mathematical Subject Classification 2000
Primary: 57M25, 57N10
##### Publication
Received: 28 February 2009
Revised: 27 June 2009
Accepted: 23 July 2009
Published: 4 May 2011
##### Authors
 William Jaco Department of Mathematics Oklahoma State University Stillwater OK 74078-1058 USA J Hyam Rubinstein Department of Mathematics and Statistics The University of Melbourne Parkville, VIC 3010 Australia Stephan Tillmann School of Mathematics and Physics The University of Queensland Brisbane, QLD 4072 Australia