Geometric moves relate geometric triangulations

Tejas Kalelkar; Advait Phanse

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arXiv · 1907.02643

Geometric moves relate geometric triangulations

Tejas Kalelkar·Advait Phanse

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Abstract

A geometric triangulation of a Riemannian manifold is a triangulation where the interior of each simplex is totally geodesic. Bistellar moves are local changes to the triangulation which are higher dimensional versions of the flip operation of triangulations in a plane. We show that geometric triangulations of a compact hyperbolic, spherical or Euclidean manifold are connected by geometric bistellar moves (possibly adding or removing vertices), after taking sufficiently many derived subdivisions. For dimensions 2 and 3, we show that geometric triangulations of such manifolds are directly related by geometric bistellar moves (without having to take derived subdivision).

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Tejas Kalelkar, Advait Phanse. 2019-07-04. Geometric moves relate geometric triangulations. https://arxiv.org/abs/1907.02643

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