Minimal triangulations for an infinite family of lens spaces

Details Minimal triangulations for an infinite family of lens spaces Minimal triangulations for an infinite family of lens spaces

2008-05-16

arxiv.org/abs/0805.2425v1

Mathematics

Geometric Topology

32 pages, 6 figures

Scientific paper

The notion of a layered triangulation of a lens space was defined by Jaco and Rubinstein in earlier work, and, unless the lens space is L(3,1), a layered triangulation with the minimal number of tetrahedra was shown to be unique and termed its "minimal layered triangulation." This paper proves that for each integer n>1, the minimal layered triangulation of the lens space L(2n,1) is its unique minimal triangulation. More generally, the minimal triangulations (and hence the complexity) are determined for an infinite family of lens spaces containing the lens spaces L(2n,1).

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