THE GEOMETRY OF THE HANDLEBODY GROUPS I: DISTORTION

DOI10.1142/S1793525312500070zbMath1244.57034arXiv1101.1838OpenAlexW2963033222MaRDI QIDQ2885381

Ursula Hamenstädt, Sebastian W. Hensel

Publication date: 23 May 2012

Published in: Journal of Topology and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.1838

zbMATH Keywords

mapping class groupshandlebody groupssubgroup distortion

Mathematics Subject Classification ID

Geometric group theory (20F65) General low-dimensional topology (57M99) Automorphisms of infinite groups (20E36) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)

Related Items (13)

On purely loxodromic actions ⋮ Right-angled Artin groups on finite subgraphs of disk graphs ⋮ Stable subgroups of the genus 2 handlebody group ⋮ Arithmetic quotients of the mapping class group ⋮ Automorphisms of the 3-sphere that preserve spatial graphs and handlebody-knots ⋮ Realisation and dismantlability ⋮ The geometry of the handlebody groups. II: Dehn functions ⋮ Filling triangulated surfaces ⋮ Arc complexes, sphere complexes, and Goeritz groups ⋮ Spotted disk and sphere graphs. I ⋮ A lower bound of the distortion of the Torelli group in the mapping class group with boundary components ⋮ Isoperimetric inequalities for the handlebody groups ⋮ Affine diffeomorphism groups are undistorted

Cites Work

• Unnamed Item
• Translation lengths in \(\text{Out}(F_n)\).
• Geometry of the mapping class groups. I: Boundary amenability
• Twist groups of compact 3-manifolds
• The length spectra as moduli for compact Riemann surfaces
• Geometry of the complex of curves. II: Hierarchical structure
• Homological stability for automorphism groups of free groups
• A combinatorial model for the Teichmüller metric
• On Homeomorphisms of a 3-Dimensional Handlebody

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