Word hyperbolic extensions of surface groups

By U. Hamenstaedt. 2005

110 citations recorded by the source corpus.

Let S be a closed surface of genus at least 2. We show that a finitely generated group G which is an extension of the fundamental group H of S is word hyperbolic if and only the orbit map of the quotient group G/H on the complex of curves is a quasi-isometric embedding.This in turn is equivalent to G/H being convex cocompact in the sense of Farb and Mosher.

Subfields: Computer Graphics and Computer-Aided Design, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cc5d30b67b3669e5b5b629c4fda52b8cc9f072dc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Graphics and Computer-Aided Design

1. Alessandro Sisto
2. Richard P. Kent
3. Johanna Mangahas
4. Christopher J. Leininger
5. Mahan Mj
6. Pranab Sardar
7. Mark F. Hagen

In Geometry and Topology

1. Alessandro Sisto
2. Mark F. Hagen
3. Pranab Sardar
4. Johanna Mangahas
5. Richard P. Kent
6. Christopher J. Leininger
7. Mahan Mj
8. Matt Clay

In Mathematical Physics

1. Alessandro Sisto
2. Mark F. Hagen
3. Pranab Sardar
4. Johanna Mangahas
5. Richard P. Kent
6. Christopher J. Leininger
7. Mahan Mj
8. Matt Clay

Citations in the corpus

• The geometry of right angled Artin subgroups of mapping class groups (2010, background): “Given an arbitrary set of elements f1, . . . , fn ∈ Mod(S), we cannot expect that they generate a free group upon raising to sufficiently high powers.”
• Shadows Of Mapping Class Groups: Capturing Convex Cocompactness (2005, background): “Remark. This theorem was independently discovered by U. Hamenst¤ adt [ 27 ].”
• A Combination Theorem for Metric Bundles (2009, methodology): “aces and occur as natural base spaces for metric bundles. See [LMS11] by Leininger-MjSchleimer for a closely related example. b) It removes the hypothesis on existence of totally geodesic sections in [Ham05] altogether. Proposition2.10ensuresthe existence ofqi sectionsundermild technical assumptions”
• Boundaries and automorphisms of hierarchically hyperbolic spaces (2016, background): “Importantly, they satisfy several strong equivalent characterizations, which we state in the following theorem-definition with parts due variously to Farb-Mosher [FM02], Hamenstädt [Ham05], Kent-Leininger [KL08], and the first author with Taylor [DT15]:”