## 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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### References:

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