On infinitely generated homology of Torelli groups

DOI10.1090/SPMJ/1838MaRDI QIDQ6665337

A. A. Gaifullin

Publication date: 17 January 2025

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

spectral sequenceTorelli grouphomology of groupscomplex of cyclesabelian cycle

Mathematics Subject Classification ID

Topological methods in group theory (57M07) Homological methods in group theory (20J05) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Cites Work

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• Generating the Torelli group
• The structure of the Torelli group. I: A finite set of generators for \({\mathcal I}\)
• Abelian and solvable subgroups of the mapping class group
• The structure of the Torelli group. III: The abelianization of \({\mathcal S}\)
• The genus 2 Torelli group is not finitely generated
• The Torelli groups for genus 2 and 3 surfaces
• The rational cohomology ring of the moduli space of abelian 3-folds.
• Cutting and pasting in the Torelli group
• The dimension of the Torelli group
• On a spectral sequence for the action of the Torelli group of genus on the complex of cycles
• Homological infiniteness of Torelli groups
• Abelian subgroups of the Torelli group
• The top homology group of the genus 3 Torelli group
• On the structure of the top homology group of the Johnson kernel

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