Related papers: Differential topology interacts with isoparametric…

In this paper we study the existence of solutions to an isotropic differential inclusion.

In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.

In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.

We consider Gaussian fields of real symmetric, complex Hermitian or quaternionic Hermitian matrices over an electrical network, and describe how the isomorphisms between these fields and random walks give rise to topological expansions…

In this note we briefly survey and propose some open problems related to isoparametric theory.

This paper studies the formal deformations of differential algebra morphisms. As a consequence, we develop a cohomology theory of differential algebra morphisms to interpret the lower degree cohomology groups as formal deformations. Then,…

We survey some results on toric topology.

In this article we introduce the topological study of codimension-1 foliations which admit contact or symplectic structures on the leaves. A parametric existence h-principle for foliated contact structures is provided for any cooriented…

We prove a Galois-type correspondence between compositions of purely inseparable field extensions (including infinite ones) and subalgebras of differential operators. This correspondence can be utilized to establish a connection between…

In this paper, we discuss foliations by real curves. We investigate differential equations which are modifications of du/dx = v along leaves. Our focus is on having a solution operator so that u is continuous if v is continuous.

We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…

In this paper we introduce the notion of deformation cohomology for singular foliations and related objects (namely integrable differential forms and Nambu structures), and study it in the local case, i.e., in the neighborhood of a point.

We review some applications of noncommutative geometry to the study of transverse geometry of Riemannian foliations and discuss open problems.

We remark some basic facts on homological aspects of involutive Lie bialgebras and their involutive bimodules, and present some problems on surface topology related to these facts.

In this paper we study transversely holomorphic foliations of complex codimension one with some hypothesis on the transverse structure.

Let (M,F) be a foliated manifold. We study the relationship between the basic cohomology Hb(M,F) of the foliation and the De Rham cohomology H(DF) of the space of leaves M/F as a quotient diffeological space. We prove that for an arbitrary…

We study tilings of the plane composed of two repeating tiles of different assigned areas relative to an arbitrary periodic lattice. We classify isoperimetric configurations (i.e., configurations with minimal length of the interfaces) both…

Differentiation has widespread applications, particularly in image processing for edge detection. Significant advances have been made in using nanophotonic structures and metamaterials to perform such operations. In particular, a recent…

In this note we study several aspects of coisotropic submanifolds of a contact manifold. In particular we give a structure theorem for the singularity of the characteristic foliation of a coisotropic submanifold. Moreover we establish the…

We review basic notions and methods of noncommutative geometry and their applications to analysis and geometry on foliated manifolds.