## Algebraic & Geometric Topology

### Coverings and minimal triangulations of $3$–manifolds

#### 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 $S3∕Q4k$ have complexity $k$, where $k≥2$. Moreover, it is shown that their minimal triangulations are unique.

#### Article information

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

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

https://projecteuclid.org/euclid.agt/1513715227

Digital Object Identifier
doi:10.2140/agt.2011.11.1257

Mathematical Reviews number (MathSciNet)
MR2801418

Zentralblatt MATH identifier
1229.57010

#### Citation

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. https://projecteuclid.org/euclid.agt/1513715227

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