Balanced triangulations on few vertices and an implementation of cross-flips

Lorenzo Venturello

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arXiv · 1811.10271

Balanced triangulations on few vertices and an implementation of cross-flips

Lorenzo Venturello

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Abstract

A $d$-dimensional simplicial complex is balanced if the underlying graph is $(d+1)$-colorable. We present an implementation of cross-flips, a set of local moves introduced by Izmestiev, Klee and Novik which connect any two PL-homeomorphic balanced combinatorial manifolds. As a result we exhibit a vertex minimal balanced triangulation of the real projective plane, of the dunce hat and of the real projective space, as well as several balanced triangulations of surfaces and 3-manifolds on few vertices. In particular we construct small balanced triangulations of the 3-sphere that are non-shellable and shellable but not vertex decomposable.

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Lorenzo Venturello. 2018-11-26. Balanced triangulations on few vertices and an implementation of cross-flips. https://arxiv.org/abs/1811.10271

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