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