# An upper bound on Pachner moves relating geometric triangulations

@article{Kalelkar2019AnUB, title={An upper bound on Pachner moves relating geometric triangulations}, author={Tejas Kalelkar and Advait Phanse}, journal={arXiv: Geometric Topology}, year={2019} }

We show that any two geometric triangulations of a hyperbolic, spherical or Euclidean manifold are related by a sequence of Pachner moves of bounded length. This bound is in terms of the dimension of the manifold, the number of top dimensional simplexes and upper and lower bounds on the lengths of edges of the triangulation. This gives an algorithm to check if two geometrically triangulated compact hyperbolic or low dimensional spherical manifolds are isometric.

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