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 $L\left(4k,2k-1\right)$ 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.