Nielsen Realization for sphere twists on 3-manifolds
Geometric Topology
2022-04-26 v2
Abstract
For a 3-manifold M, the twist group Twist(M) is the subgroup of the mapping class group Mod(M) generated by twists about embedded 2-spheres. We study the Nielsen realization problem for subgroups of Twist(M). We prove that a nontrivial subgroup G<Twist(M) is realized by diffeomorphisms if and only if G is cyclic and M is a connected sum of lens spaces. We also apply our methods to the Burnside problem for 3-manifolds and show that Diff(M) does not contain an infinite torsion group when M is reducible and not a connected sum of lens spaces.
Cite
@article{arxiv.2204.04820,
title = {Nielsen Realization for sphere twists on 3-manifolds},
author = {Lei Chen and Bena Tshishiku},
journal= {arXiv preprint arXiv:2204.04820},
year = {2022}
}
Comments
16 pages; v2: added a computation of the twist group for an arbitrary 3-manifold and added an application to the Burnside problem for Diff(M)