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 S 3 =Q 4k have complexity k , where k 2. Moreover, it is shown that their minimal triangulations are unique.