Rank-1 phenomena for mapping class groups

DOI10.1215/S0012-7094-01-10636-4zbMath1025.20023OpenAlexW2031571526WikidataQ57254104 ScholiaQ57254104MaRDI QIDQ1847806

Yair N. Minsky, Benson Farb, Alexander Lubotzky

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-01-10636-4

zbMATH Keywords

representationsouter automorphism groupsfree groupslatticesprofinite completionsmapping class groupspro-\(p\) groupslinear growth\(p\)-adic analytic groupsrank 1boundedly generated groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Topological methods in group theory (57M07) Structure of modular groups and generalizations; arithmetic groups (11F06) Chains and lattices of subgroups, subnormal subgroups (20E15) Automorphism groups of groups (20F28) Free nonabelian groups (20E05) Teichmüller theory for Riemann surfaces (30F60) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)

Related Items

Mapping class groups and outer automorphism groups of free groups are \(C^{*}\)-simple ⋮ Stable commutator length of a Dehn twist ⋮ Failure of separation by quasi-homomorphisms in mapping class groups ⋮ A Gauss-Bonnet formula for moduli spaces of Riemann surfaces ⋮ Distortion elements for surface homeomorphisms ⋮ Quasi-homomorphisms and stable lengths in mapping class groups ⋮ The Thurston boundary of Teichmüller space and complex of curves ⋮ Boundaries and automorphisms of hierarchically hyperbolic spaces ⋮ Distortion for abelian subgroups of Out(Fn) ⋮ Large-scale rigidity properties of the mapping class groups ⋮ Heegaard splittings with large subsurface distances ⋮ Filling loops at infinity in the mapping class group ⋮ Right-angled Artin groups and a generalized isomorphism problem for finitely generated subgroups of mapping class groups ⋮ Low‐dimensional linear representations of mapping class groups ⋮ Constructing group actions on quasi-trees and applications to mapping class groups ⋮ Geometry and rigidity of mapping class groups. ⋮ Local topology in deformation spaces of hyperbolic 3-manifolds ⋮ Distortion and Tits alternative in smooth mapping class groups ⋮ Actions of solvable Baumslag-Solitar groups on surfaces with (pseudo)-Anosov elements ⋮ Divergence in lattices in semisimple Lie groups and graphs of groups ⋮ Limit sets of Teichmüller geodesics with minimal nonuniquely ergodic vertical foliation. II ⋮ Reduction theory for mapping class groups and applications to moduli spaces ⋮ Pseudo–Anosov mapping classes from pure mapping classes ⋮ Geometry of the mapping class groups. I: Boundary amenability ⋮ Two questions on mapping class groups ⋮ Convex cocompact subgroups of mapping class groups ⋮ Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity. ⋮ Any Baumslag–Solitar action on surfaces with a pseudo-Anosov element has a finite orbit ⋮ Higher dimensional divergence for mapping class groups ⋮ Divergence, undistortion and Hölder continuous cocycle superrigidity for full shifts ⋮ Affine diffeomorphism groups are undistorted ⋮ On visualization of the linearity problem for mapping class groups of surfaces ⋮ Distortion elements in group actions on surfaces

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