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.
Boldsen & M
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
We show for g > 6 that the second homology group of the Torelli group of a surface of genus g and 1 boundary component is generated as an Sp(2g,Z)-module by the image under the stabilization map of the second homology group of the Torelli group of a surface of genus 6 and 1 boundary component. In the process we also show that the quotient of the complex of arcs with identity permutation by the Torelli group is (g-2)-connected, for one or two boundary components.
citation-role summary
background 1
citation-polarity summary
fields
math.GT 2years
2026 2verdicts
UNVERDICTED 2roles
background 1polarities
background 1representative citing papers
An exposition of the calculation of the second rational cohomology group of the Torelli group using the Johnson homomorphism and two key prior results.
citing papers explorer
-
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.
-
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.