Most big mapping class groups fail the Tits Alternative
Group Theory
2022-01-05 v1
Abstract
Let be a surface, possibly with boundary. Suppose it has infinite genus or infinitely many punctures, or a closed subset which is a disk with a Cantor set removed from its interior. For example, could be any surface of infinite type with only finitely many boundary components. We prove that the mapping class group of does not satisfy the Tits Alternative. That is, Map contains a finitely generated subgroup that is not virtually solvable and contains no nonabelian free group.
Cite
@article{arxiv.2012.01310,
title = {Most big mapping class groups fail the Tits Alternative},
author = {Daniel Allcock},
journal= {arXiv preprint arXiv:2012.01310},
year = {2022}
}