Volume 11, issue 3 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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(4k,2k 1) and the generalised quaternionic space S3Q4k have complexity k, where k 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
References
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