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Bounds on Pachner moves and systole lengths for cusped hyperbolic 3-manifolds

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Sriram Raghunath (Rutgers)

Abstract: Any two topological triangulations of a 3-manifold are related by a finite number of Pachner moves, but the best-known upper bounds on this number are huge and involve towers of exponentials in the number of tetrahedra in the triangulation. We give a sharper upper bound on the number of Pachner moves relating two geometric ideal triangulations of a cusped hyperbolic 3-manifold by exploiting the hyperbolic geometry of the cusped manifold. We also apply these geometric methods to prove a lower bound on the systole length for cusped hyperbolic 3-manifolds. This is joint work with Tejas Kalelkar.