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Minimal triangulations for an infinite family of lens spaces. (English) Zbl 1227.57026

Summary: The notion of a layered triangulation of a lens space was defined by Jaco and Rubinstein, 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 \(n \geqslant 2\), 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 space of the form \(L(2n, 1)\).

MSC:

57N10 Topology of general \(3\)-manifolds (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57Q15 Triangulating manifolds
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