1996/09/13 by David Gabai, Gabai, David, G. Robert Meyerhoff +3 · 2 citations
Mathematics · Physics and Astronomy · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematics and Applications #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.math/9609207
openalex publication_date 1996/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper introduces a rigorous computer-assisted procedure for analyzing hyperbolic 3-manifolds. This technique is used to complete the proof of several long-standing rigidity conjectures in 3-manifold theory as well as to provide a new lower bound for the volume of a closed orientable hyperbolic 3-manifold. We prove the following result: \it\noindent Let N be a closed hyperbolic 3-manifold. Then \beginenumerate \item[(1)] If f\colon M → N is a homotopy equivalence where M is a closed irreducible 3-manifold, then f is homotopic to a homeomorphism. \item[(2)] If f,g\colon M→ N are homotopic homeomorphisms, then f is isotopic to g. \item[(3)] The space of hyperbolic metrics on N is path connected. \endenumerate