Thurston’s ending lamination conjecture proposes that a finitelygenerated Kleinian group is uniquely determined (up to isometry) by the topology of its quotient and a list of invariants that describe the asymptotic geometry of its ends. We present a proof of this conjecture for punctured-torus groups. These are free two-generator Kleinian groups with parabolic commutator, which should be though...

We characterize positive topological entropy for quasi-state space homeomorphisms induced from C∗-algebra automorphisms in terms of dynamically generated subspaces isomorphic to l1. This geometric condition is also used to give a description of the topological Pinsker algebra. In particular we obtain a geometric characterization of positive entropy for topological dynamical systems, as well as ...

We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of t...

In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalities in Hausdorff topological vector spaces. By means of fixed point theorem, we obtain existence theorem for the system of generalized vector quasi-variational-like inequalities and also derive the existence result of solutions for the generalized vector quasi-variational-like inequalities. Ke...

We study the quotients of the Toeplitz C*-algebra of a quasi-lattice ordered group (G, P ), which we view as crossed products by a partial actions of G on closed invariant subsets of a totally disconnected compact Hausdorff space, the Nica spectrum of (G, P ). Our original motivation and our main examples are drawn from right-angled Artin groups, but many of our results are valid for more gener...

Topological crystalline insulators are phases of matter where the symmetries solely protect topology. In this work, we explore effect many-body interactions in a subclass topological insulators, namely mirror-symmetry protected insulator. Employing prototypical mirror-symmetric quasi-one-dimensional model, demonstrate emergence phase and its robustness presence short-range interactions. When lo...

It is well-known that no knot can be cancelled in a connected sum with another knot, whereas every link up to link homotopy can be cancelled in a (componentwise) connected sum with another link. In this paper we address the question whether some form of the ‘complexity accumulation’ property of knots holds for (piecewiselinear) links up to some stronger analogue of link homotopy, which still do...