The second rational homology of the Torelli group

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Daniel Minahan , Andrew Putman This is my paper · ORCID

classification math.GTmath.AT

keywords grouphomologyrationalsecondtorellicalculate

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abstract

We calculate the second rational homology group of the Torelli group for $g \geq 6$.

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The Birman--Craggs--Johnson homomorphism and the handlebody Torelli group
math.GT 2026-07 conditional novelty 6.0 of 10

For genus at least 3, the BCJ image of the handlebody Torelli group is an explicit monomial subspace B^bi_3, and of the Johnson kernel is B^bi_2; cup-product lower bounds of order g^6 and g^4 follow.
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...