相关论文: Measurable versions of the LS category on laminati…

A version of the tangential LS category is introduced for topological laminations with a transverse invariant measure. Here, we use the transverse measure of the contraction of a tangential categorical open set instead of counting this set.…

In the author's Ph.D., a version of the tangential LS category for foliated spaces depending on a transverse invariant measure, called the measured category, was introduced. Unfortunately, the measured category vanishes easily. When it is…

In [Mor], we have introduced a notion of flat laminations on surfaces endowed with a flat structure, similar to geodesic laminations on hyperbolic surfaces. Here is a sequel to this article that aims at defining transversal measures on flat…

We describe a construction of ordered algebraic structures (ordered abelian semigroups, ordered commutative semirings, etc.) and describe applications to codimension-1 laminations. For a suitable ordered semi- algebraic structure $\mathbb…

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…

Classical Ljusternik-Schnirelmann category is upper bounded by the number of critical points of any bounded from below differentiable functions of Palais-Smale type. Here we achieve an adaptation of this result for the tangential category…

We study the transverse Lusternik-Schnirelmann category of a Riemannian foliation on a compact manifold. We obtain a necessary and sufficient condition when the transverse LS category is finite. We also introduce a variation on the concept…

We exhibit the duality between best Lipschitz (infinity harmonic) maps and least gradient maps in the case of maps from surfaces to the circle. We show that given a homotopy class of a map from a surface to the circle the infinity harmonic…

We introduce the so-called BT-category of borelian-topological spaces: it will be a natural frame for a measurable classification of usual foliations and laminations. We focus on the two-dimensional case: borelian laminations by surfaces.…

Since their introduction by Thurston, measured geodesic laminations on hyperbolic surfaces occur in many contexts. In [Mor], we have introduced a notion of flat laminations on surfaces endowed with a half-translation structure (that is a…

Pointwise tangential dimensions are introduced for metric spaces. Under regularity conditions, the upper, resp. lower, tangential dimensions of X at x can be defined as the supremum, resp. infimum, of box dimensions of the tangent sets, a…

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…

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,…

We study the lower bounds and upper bounds for LS-category and equivariant LS-category. In particular we compute both invariants for torus manifolds. There are some examples to show the sharpness of conditions in the theorems. Moreover the…

In recent work, Harman and Snowden introduced a notion of measure on a Fra\"iss\'e class $\mathfrak{F}$, and showed how such measures lead to interesting tensor categories. Constructing and classifying measures is a difficult problem, and…

A new notion of cohomology is introduced for MT-spaces, which are measurable and topological spaces whose measurable structure may not agree with the Borel $\sigma$-algebra of their topology. The main examples of MTspaces are measurable…

There are two definitions of the measurable functional on the topological vector space: as a linear and measurable real-valued function and as a pointwise limit of the sequence of the continious linear functionals. In general case they are…

In this paper, we introduce relative LS category of a map and study some of its properties. Then we introduce `higher topological complexity' of a map, a homotopy invariant. We give a cohomological lower bound and compare it with previously…

We determine which tangential varieties of homogeneously embedded rational homogeneous varieties are spherical. We determine the homogeneous coordinate rings and rings of covariants of the tangential varieties of homogenously embedded…

In recent work, Harman and Snowden constructed a symmetric tensor category associated to an oligomorphic group equipped with a measure. The oligomorphic group $\mathbb{G}$ of order preserving automorphisms of the real line admits exactly…