The second rational homology of the Torelli group is finitely generated

2023/07/13 by Daniel Minahan, Minahan, Daniel · 2 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2307.07082

Abstract

We prove that second rational homology of the Torelli group of an orientable closed surface of genus g is finite dimensional for g at least 51. This rules out the simplest obstruction to the Torelli group being finitely presented and provides a partial answer to a question of Bestvina.

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• On torsion in the homology of the Torelli group
• Finite generation of abelianizations of the genus 3 Johnson kernel and the commutator subgroup of the Torelli group for Out(F₃)

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