The twist-cofinite topology on the mapping class group of a surface
Geometric Topology
2025-08-06 v2 Group Theory
Abstract
A topology is defined on the mapping class group of a compact connected orientable surface. It is shown that a notion of "genericity" on subsets of the mapping class group arises from this definition. Many plausible results follow from this notion easily; for example, the set of pseudo-Anosov maps is shown to be generic, and can be assumed to have arbitrary large stretch factor, generically. Let M be a 3-manifold obtained from a Heegaard splitting of fixed genus g and generic gluing map. It is shown that for such manifolds, generically M is hyperbolic, has first Betti number zero and Heegaard genus exactly equal to g.
Keywords
Cite
@article{arxiv.2003.11212,
title = {The twist-cofinite topology on the mapping class group of a surface},
author = {Ingrid Irmer},
journal= {arXiv preprint arXiv:2003.11212},
year = {2025}
}