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 and convex cocompact, called a Schottky ...

In this paper, we classify 2-closed (in Wielandt’s sense) permutation groups which contain a normal regular cyclic subgroup and prove that for each such group G, there exists a circulant Γ such that Aut(Γ) = G.

We introduce discrete-time linear control systems on connected Lie groups and present an upper bound for the outer invariance entropy of admissible pairs ( K , Q ). If stable subgroup uncontrolled system is closed has positive measure a left invariant Haar measure, coincides with entropy.

We consider induced coactions on C*-algebras along a homomorphism of locally compact quantum groups which need not give closed subgroup. Our approach generalizes the constructed by Vaes, and also includes certain fixed point algebras. focus case when satisfies analogue properness. Induced such still admit natural formulations various properties known in subgroup, as imprimitivity adjointness wi...

We prove that any Lie subgroup G (with finitely many connected components) of an infinite-dimensional topological group which is amalgamated product two closed subgroups can be conjugated to one factor. apply this result classify actions on Danielewski surfaces by elements the overshear (up conjugation).

Let X be a proper hyperbolic geodesic metric space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is not elementary then for every p ∈ (1, ∞) the second continuous bounded cohomology group H 2 cb (G, L p (G)) does not vanish. As an application, we derive some structure results for closed subgroups of Iso(X).

For G a closed subgroup of S∞, we provide a precise combinatorial characterization of when the universal minimal flow M(G) is metrizable. In particular, each such instance fits into the framework of metrizable flows developed in [KPT] and [NVT]; as a consequence, each G with metrizable universal minimal flow has the generic point property, i.e. every minimal G-flow has a point whose orbit is co...

Every permutation invariant Borel subset of the space of countable structures is definable in Lω1ω by a theorem of Lopez-Escobar. We prove variants of this theorem relative to fixed relations and fixed non-permutation invariant quantifiers. Moreover we show that for every closed subgroup G of the symmetric group S∞, there is a closed binary quantifier Q such that the G-invariant subsets of the ...

Let X be a proper hyperbolic geodesic metric space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is not elementary then for every p ∈ (1, ∞) the second continuous bounded cohomology group H 2 cb (G, L p (G)) does not vanish. As an application, we derive some structure results for closed subgroups of Iso(X).