Work

Nielsen realization for sphere twists on 3-manifolds

Year: 2025

Type: article

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, including S 1 × S 2 . 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.

Source: Israel Journal of Mathematics

DOI: 10.1007/s11856-025-2813-3

Authors: Lei Chen, Bena Tshishiku

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science, Brown University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

OpenAlex ID: W4414921013