The girth alternative for mapping class groups.

DOI10.4171/GGD/223zbMath1323.20034arXiv1105.5422MaRDI QIDQ2016101

Kei Nakamura

Publication date: 19 June 2014

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.5422

zbMATH Keywords

finitely generated groupsmapping class groupsgirth of Cayley graphsvirtually free-Abelian groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Topological methods in group theory (57M07) Group actions on manifolds and cell complexes in low dimensions (57M60) Residual properties and generalizations; residually finite groups (20E26)

Cites Work

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• Expansion in \(\text{SL}_d(\mathbb Z/q\mathbb Z)\), \(q\) arbitrary.
• The girth of groups satisfying Tits alternative.
• Free limits of Thompson's group \(F\).
• Abelian and solvable subgroups of the mapping class group
• The free group of rank 2 is a limit of Thompson's group \(F\).
• Groups of piecewise linear homeomorphisms of the real line
• Ramanujan graphs
• Maximal subgroups of infinite index in finitely generated linear groups
• Explicit constructions of graphs without short cycles and low density codes
• On the girth of finitely generated groups.
• Uniform uniform exponential growth of subgroups of the mapping class group
• Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).
• Amenable groups and varieties of groups
• Thurston's Work on Surfaces (MN-48)

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