English

Random methods in 3-manifold theory

Geometric Topology 2014-05-27 v1 Group Theory Probability

Abstract

We show that for any integers k and g, with g at least two, there are infinitely many closed hyperbolic 3-manifolds which are integral homology spheres with Casson invariant k, and Heegaard genus equal to g. This existence result is shown using random methods, using a model of random 3-manifolds arising from random walks on the mapping class group of a closed orientable surface.

Keywords

Cite

@article{arxiv.1405.6410,
  title  = {Random methods in 3-manifold theory},
  author = {Alexander Lubotzky and Joseph Maher and Conan Wu},
  journal= {arXiv preprint arXiv:1405.6410},
  year   = {2014}
}

Comments

34 pages, 8 figures

R2 v1 2026-06-22T04:22:56.392Z