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The second rational homology of the Torelli group
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The second rational homology of the Torelli group
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We calculate the second rational homology group of the Torelli group for $g \geq 6$.
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Cited by 4 Pith papers
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Finite generation, algebraicity, and representation stability for homology of Torelli groups
Proves finite generation of H_k(I_g; Z) for k ≤ g-2 and that rational homology is an algebraic Sp(2g,Z)-representation, turning conditional cohomology computations into theorems and proving Morita's conjecture.
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The Birman--Craggs--Johnson homomorphism and the handlebody Torelli group
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.
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Torsion in the homology of the Torelli group and the Birman-Craggs-Johnson homomorphism
The Birman-Craggs-Johnson homomorphism is injective on the subgroup of H_k(I_g) generated by abelian cycles from disjoint separating Dehn twists, for k ≤ g-2.
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Calculating the second rational cohomology group of the Torelli group
An exposition of the calculation of the second rational cohomology group of the Torelli group using the Johnson homomorphism and two key prior results.
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