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math.GTMay 1, 2019
6
citations (OpenAlex)
authors
  • Gabriele Viaggi
institutions
  • Heidelberg University
arXiv abstractPDF
paper

Volumes of random 3-manifolds

arXiv:1905.04935 · doi:10.1112/topo.12190

Abstract

We prove a law of large numbers for the volumes of families of random hyperbolic mapping tori and Heegaard splittings providing a sharp answer to a conjecture of Dunfield and Thurston.

arXiv comment30 pages, 5 figures. Correction on the assumptions on the probability measure in the introduction. Added discussion in section 4.4

References in corpus (14)

  • Geometry of the Complex of Curves I: Hyperbolicity
  • Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle
  • Random walks on the mapping class group
  • Finite covers of random 3-manifolds
  • A characterization of short curves of a Teichmueller geodesic
  • Random Heegaard splittings
  • Hyperbolicity in Teichmüller space
  • Sublinear deviation between geodesics and sample paths
  • Geometric inflexibility and 3-manifolds that fiber over the circle
  • Statistics of Random 3-Manifolds occasionally fibering over the circle
  • Bounded combinatorics and uniform models for hyperbolic 3-manifolds
  • The Smallest Positive Eigenvalue Of Fibered Hyperbolic 3-Manifolds
  • Small eigenvalues of random 3-manifolds
  • The compression body graph has infinite diameter

Cited by in corpus (1)

  • Uniform models and short curves for random 3-manifolds
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