Related papers: LS category on laminations with transverse invaria…

Since their introduction by Thurston, measured geodesic laminations on hyperbolic surfaces occur in many contexts. In this survey, we give a generalization of geodesic laminations on surfaces endowed with a half-translation structure,…

A measured laminations on the universal hyperbolic solenoid $\S$ is, by our definition, a leafwise measured lamination with appropriate continuity for the transverse variations. An earthquakes on theuniversal hyperbolic solenoid $\S$ is…

Implementing an idea due to John Baez and James Dolan we define new invariants of Whitney stratified manifolds by considering the homotopy theory of smooth transversal maps. To each Whitney stratified manifold we assign transversal homotopy…

For a compact riemannian manifold of negative curvature, the geodesic foliation of its unit tangent bundle is independent of the negatively curved metric, up to Holder bicontinuous homeomorphism. However, the riemannian metric defines a…

Let $\mathcal{F}$ be a compact Hausdorff foliation on a compact manifold. Let ${E_2^{>0,\bullet}}=\oplus\{E_2^{p,q}\colon p>0,q\geq 0\}$ be the subalgebra of cohomology classes with positive transverse degree in the $E_2$ term of the…

We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…

We prove that if F is a foliation of a compact manifold M with all leaves compact submanifolds, and the transverse saturated category of F is finite, then the leaf space M/F is compact Hausdorff. The proof is surprisingly delicate, and is…

The category $\bcalNT$ is a category of certain commutative graded algebras over a field. It was introduced in \cite{Lobos2} as a generalization of algebras generated by Jucys-Murphy elements in the many \textbf{End} algebras of the…

We prove that a transversely holomorphic foliation which is transverse to the fibers of a fibration, is a Seifert fibration if the set of compact leaves is not of zero measure. Similarly, we prove that a finitely generated subgroup of…

Thurston parameterized quadratic invariant laminations with a non-invariant lamination, the quotient of which yields a combinatorial model for the Mandelbrot set. As a step toward generalizing this construction to cubic polynomials, we…

We introduce the notion of a relative spherical category. We prove that such a category gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants defined in arXiv:1008.3103 and arXiv:0910.1624, respectively. In this…

We consider a transversally conformal foliation $\mathcal{F}$ of a closed manifold $M$ endowed with a smooth Riemannian metric whose restriction to each leaf is negatively curved. We prove that it satisfies the following dichotomy. Either…

For a non-elementary subgroup of the mapping class group of a surface, we study its invariant Radon measures on the space of measured laminations, by classifying them on the recurrent measured laminations. In particular, given a…

Thurston defined invariant laminations, i.e. collections of chords of the unit circle $S^1$ (called \emph{leaves}) that are pairwise disjoint inside the open unit disk and satisfy a few dynamical properties. To be directly associated to a…

It is shown that some convolution semigroups of infinitely divisible measures are invariant under the random integral mappings $I^{h,r}_{(a,b]}$ defined in $(\star)$ below. The converse implication is specified for the semigroups of…

Simple semitoric systems were classified about ten years ago in terms of a collection of invariants, essentially given by a convex polygon with some marked points corresponding to focus-focus singularities. Each marked point is endowed with…

A generalization of an inverse system in a category was recently introduced, as well as that of the corresponding pro-category These so called the delay-inverse systems and delay-pro-category could potentially yield a new theory of (delay-)…

We develop the theory of categories of measurable fields of Hilbert spaces and bounded fields of bounded operators. We examine classes of functors and natural transformations with good measure theoretic properties, providing in the end a…

We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable 3-manifold is trivialisable. This invariant is strong…

A connection between representation of compact groups and some invariant ensembles of Hermitian matrices is described. We focus on two types of invariant ensembles which extend the Gaussian and the Laguerre Unitary ensembles. We study them…