The Homeomorphism Problem For Hyperbolic Manifolds I

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.

v1, 44 pages, 13 figures, comments/corrections welcome

References in corpus (4)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Algorithmic homeomorphism of 3-manifolds as a corollary of geometrization
• The homeomorphism problem for closed 3-manifolds