Nielsen Realization for sphere twists on 3-manifolds

Lei Chen; Bena Tshishiku

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arXiv · 2204.04820

Nielsen Realization for sphere twists on 3-manifolds

Lei Chen·Bena Tshishiku

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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.

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BibTeX RIS

Lei Chen, Bena Tshishiku. 2022-04-11. Nielsen Realization for sphere twists on 3-manifolds. https://arxiv.org/abs/2204.04820

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