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

Lei Chen; Vladimir Markovic

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arXiv · 1904.09490

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

Lei Chen·Vladimir Markovic

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Abstract

Nielsen realization problem for the mapping class group $\text{Mod}(S_g)$ asks whether the natural projection $p_g: \text{Homeo}_+(S_g)\to \text{Mod}(S_g)$ 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 $\text{Mod}(S_g)$. The main result of this paper is that the Torelli group has no realization inside the area-preserving homeomorphisms.

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Lei Chen, Vladimir Markovic. 2019-04-20. Non-realizability of the Torelli group as area-preserving homeomorphisms. https://arxiv.org/abs/1904.09490

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