The Homeomorphism Problem For Hyperbolic Manifolds I

Joe Scull

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arXiv · 2108.00779

The Homeomorphism Problem For Hyperbolic Manifolds I

Joe Scull

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Abstract

We give a bounded runtime solution to the homeomorphism problem for closed hyperbolic 3-manifolds. This is an algorithm which, given two triangulations of hyperbolic 3-manifolds by at most $t$ tetrahedra, decides if they represent the same hyperbolic 3-manifold with runtime bounded by \[ 2^{2^{t^{O(t)}}}.\] We do this by first finding a hyperbolic structure on each manifold given as a geometric triangulation and then comparing the two as geometric manifolds.

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Joe Scull. 2021-08-02. The Homeomorphism Problem For Hyperbolic Manifolds I. https://arxiv.org/abs/2108.00779

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