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.
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