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- Benson Farb, Lee Mosher
- 2001

We develop a theory of convex cocompact subgroups of the mapping class group MCG of a closed, oriented surface S of genus at least 2, in terms of the action on Teichmüller space. Given a subgroup G of MCG de ning an extension 1 ! 1(S) ! ΓG ! G ! 1, we prove that if ΓG is a word hyperbolic group then G is a convex cocompact subgroup of MCG. When G is free… (More)

- Jeffrey Brock, Benson Farb
- 2001

Let S be a surface with genus g and n boundary components and let d(S) = 3g − 3 + n denote the number of curves in any pants decomposition of S. We employ metric properties of the graph of pants decompositions CP(S) prove that the Weil-Petersson metric on Teichmüller space Teich(S) is Gromov-hyperbolic if and only if d(S) ≤ 2. When d(S) ≥ 3 the… (More)

- Benson Farb
- 2006

This paper presents a number of problems about mapping class groups and moduli space. The paper will appear in the book Problems on Mapping Class Groups and Related Topics, ed. by B. Farb, Proc. Symp. Pure Math. series, Amer. Math. Soc.

- Thomas Church, Benson Farb
- 2010

We introduce the idea of representation stability (and several variations) for a sequence of representations Vn of groups Gn. A central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability. This makes it possible to extend classical theorems of homological stability to a much… (More)

- Benson Farb
- 2008

We describe a connection between the combinatorics of generators for certain groups and the combinatorics of Helly’s 1913 theorem on convex sets. We use this connection to prove fixed point theorems for actions of these groups on nonpositively curved metric spaces. These results are encoded in a property that we introduce called “property FAr”, which… (More)

- RESEARCH ANNOUNCEMENT, Benson Farb, Nikolai V. Ivanov
- 2004

Let S be a closed orientable surface of genus g. The mapping class group Mod(S) of S is defined as the group of isotopy classes of orientationpreserving diffeomorphisms S → S. We will need also the extended mapping class group Mod±(S) of S which is defined as the group of isotopy classes of all diffeomorphisms S → S. Let us fix an orientation of S. Then the… (More)

- ALEX ESKIN, BENSON FARB
- 1997

In this paper we use elementary geometrical and topological methods to study some questions about the coarse geometry of symmetric spaces. Our results are powerful enough to apply to noncocompact lattices in higher rank symmetric spaces, such as SL(n,Z), n ≥ 3 : Theorem 8.1 is a major step towards the proof of quasiisometric rigidity of such lattices ([E]).… (More)

In this paper we introduce and develop the theory of FI-modules. We apply this theory to obtain new theorems about: • the cohomology of the configuration space of n distinct ordered points on an arbitrary manifold; • the diagonal coinvariant algebra on r sets of n variables; • the cohomology and tautological ring of the moduli space of n-pointed curves; •… (More)

- Benson Farb, John Franks
- 2001

This self-contained paper is part of a series [FF1, FF2] seeking to understand groups of homeomorphisms of manifolds in analogy with the theory of Lie groups and their discrete subgroups. Plante-Thurston proved that every nilpotent subgroup of Diff(S) is abelian. One of our main results is a sharp converse: Diff(S) contains every finitely-generated,… (More)

- BENSON FARB
- 2000

We prove that every element of the mapping class group g has linear growth (confirming a conjecture of N. Ivanov) and that g is not boundedly generated. We also provide restrictions on linear representations of g and its finite index subgroups.