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The second rational homology of the Torelli group is finitely generated

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arxiv 2307.07082 v2 pith:SYUCCQRW submitted 2023-07-13 math.GT

Daniel Minahan This is my paper · ORCID
classification math.GT
keywords grouptorellifinitelyhomologyrationalsecondanswerbestvina
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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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  1. On torsion in the homology of the Torelli group

    math.GT 2025-10 conditional novelty 6.0 of 10

    Abelian cycles from separating-curve Dehn twists in Torelli-group homology are 2-torsion in every degree, vanish when the number of curves reaches the genus, and span a finite-dimensional space in degree 2 for genus a...

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