Non-realizability of the Torelli group as area-preserving homeomorphisms

2019/04/20 by Lei Chen, Chen, Lei, Vladimir Marković +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1904.09490

openalex publication_date 2019/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Nielsen realization problem for the mapping class group Mod(S_g) asks whether the natural projection p_g: Homeo₊(S_g)→ Mod(S_g) has a section. While all the previous results use torsion elements in an essential way, in this paper, we focus on the much more difficult problem of realization of torsion-free subgroups of Mod(S_g). The main result of this paper is that the Torelli group has no realization inside the area-preserving homeomorphisms.

Citations

• A periodicity criterion and the section problem on the Mapping Class Group

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• The Nielsen Realization Problem for Non-Orientable Surfaces
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