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- THOMAS KOBERDA, T. KOBERDA
- 2012

Consider the mapping class group Modg,p of a surface Σg,p of genus g with p punctures, and a finite collection {f1, . . . , fk} of mapping classes, each of which is either a Dehn twist about a simple closed curve or a pseudo-Anosov homeomorphism supported on a connected subsurface. In this paper we prove that for all sufficiently large N , the mapping… (More)

- THOMAS KOBERDA, T. KOBERDA
- 2009

We study the action of the mapping class group on the integral homology of finite covers of a topological surface. We use the homological representation of the mapping class to construct a faithful infinite–dimensional representation of the mapping class group. We show that this representation detects the Nielsen–Thurston classification of each mapping… (More)

- THOMAS KOBERDA
- 2011

In this article we study the right-angled Artin subgroups of a given right-angled Artin group. Starting with a graph Γ, we produce a new graph through a purely combinatorial procedure, and call it the extension graph Γ of Γ. We produce a second graph Γ k , the clique graph of Γ, by adding extra vertices for each complete subgraph of Γ. We prove that each… (More)

We prove that finitely generated purely loxodromic subgroups of a right-angled Artin group A(Γ) fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups Mod(S). In particular, such subgroups are quasiconvex in A(Γ). In addition, we identify a milder condition for a finitely generated subgroup of A(Γ) that… (More)

- THOMAS KOBERDA, T. KOBERDA
- 2011

We study the residual properties of geometric 3–manifold groups. In particular, we study conditions under which geometric 3–manifold groups are virtually residually p for a prime p, and conditions under which they are residually torsion–free nilpotent. We show that for every prime p, every geometric 3–manifold group is virtually residually p. We show that… (More)

- Thomas Koberda, T. KOBERDA
- 2011

In this article we study the space of leftand bi-invariant orderings on a torsion-free nilpotent group G. We will show that generally the set of such orderings is equipped with a faithful action of the automorphism group of G. We prove a result which allows us to establish the same conclusion when G is assumed to be merely residually torsion-free nilpotent.… (More)

- THOMAS KOBERDA, RAMANUJAN SANTHAROUBANE
- 2016

We prove that for each sufficiently complicated orientable surface S , there exists an infinite image linear representation ρ of π1(S ) such that if γ ∈ π1(S ) is freely homotopic to a simple closed curve on S , then ρ(γ) has finite order. Furthermore, we prove that given a sufficiently complicated orientable surface S , there exists a regular finite cover… (More)

- THOMAS KOBERDA, T. KOBERDA
- 2013

These are notes for a course offered at Yale University in the spring semester of 2013.

Let p : Σ → Σ be a finite Galois cover, possibly branched, with Galois group G. We are interested in the structure of the cohomology of Σ as a module over G. We treat the cases of branched and unbranched covers separately. In the case of branched covers, we give a complete classification of possible module structures of H1(Σ , C). In the unbranched case, we… (More)

- THOMAS KOBERDA
- 2012

Let X be a finite CW complex. We show that the fundamental group of X is large if and only if there is a finite cover Y of X and a sequence of finite abelian covers {YN} of Y which satisfy b1(YN ) ≥ N . We give some applications of this result to the study of hyperbolic 3–manifolds, mapping classes of surfaces and combinatorial group theory.