The complex of partial bases for \(F_n\) and finite generation of the Torelli subgroup of \(\Aut(F_n)\).

DOI10.1007/s10711-012-9765-6zbMath1294.20041arXiv1012.1914OpenAlexW2040013776MaRDI QIDQ1953086

Andrew Putman, Matthew B. Day

Publication date: 7 June 2013

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.1914

zbMATH Keywords

automorphism groups of free groupsmapping class groupsTorelli groupcurve complexes

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Topological methods in group theory (57M07) Automorphisms of infinite groups (20E36) Free nonabelian groups (20E05)

Related Items

On finite generation of the Johnson filtrations, Palindromic automorphisms of free nilpotent groups, On the second homology group of the Torelli subgroup of \(\Aut(F_n)\), On the geometry of the edge splitting complex., Effective finite generation for \([\mathrm{IA}_n,\mathrm{IA}_n\) and the Johnson kernel], The complex of partial bases of a free group, Hyperbolicity of the complex of free factors., Generating the Johnson filtration, A small normal generating set for the handlebody subgroup of the Torelli group, Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at \(t=-1\)

Cites Work

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• The free splitting complex of a free group. I: Hyperbolicity.
• A Birman exact sequence for \(\Aut(F_n)\).
• The second rational homology group of the moduli space of curves with level structures
• The Johnson homomorphism and its kernel
• A presentation for the special automorphism group of a free group
• The structure of the Torelli group. I: A finite set of generators for \({\mathcal I}\)
• A note on the connectivity of certain complexes associated to surfaces
• Geometric intersection number and analogues of the curve complex for free groups.
• An infinite presentation of the Torelli group
• A hyperbolic \(\text{Out}(F_n)\)-complex.
• Stability of the homology of the mapping class groups of orientable surfaces
• Some finitely presented subgroups of the automorphism group of a free group
• Geometry of the complex of curves. I: Hyperbolicity
• Automorphisms of free groups with boundaries.
• Homological stability for automorphism groups of free groups
• Hyperbolicity of the complex of free factors.
• Cutting and pasting in the Torelli group
• Dimension of the Torelli group for \(\text{Out}(F_n)\).
• On Siegel's modular group
• Two Theorems on the Mapping Class Group of a Surface
• Cerf Theory for Graphs
• Mapping class groups and their relationship to braid groups