Related papers: Differential topology interacts with isoparametric…
We study differential geometric properties of cuspidal edges with boundary. There are several differential geometric invariants which are related with the behavior of the boundary in addition to usual differential geometric invariants of…
This is a book on derived foliations, that are a generalisation of classical foliations in the context of derived geometry. The text starts with the basic definitions and constructions, then explore foliated cohomology (with crystal…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
We conclude the classification of isoparametric (or equivalently, polar) foliations of complex and quaternionic projective spaces. This is done by investigating the projections of certain inhomogeneous isoparametric foliations of the…
We show the equivalence of several notions in the theory of taut foliations and the theory of tight contact structures. We prove equivalence, in certain cases, of existence of tight contact structures and taut foliations.
Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…
We discuss some properties of the distance functions on Riemannian manifolds and we relate their behavior to the geometry of the manifolds. This leads to alternative proofs of some "classical" theorems connecting curvature and topology.
We establish the leafwise intersection property for closed, coisotropic submanifolds in an exact symplectic manifold satisfying natural additional assumptions.
This is a survey article on the relationship between algebraic properties of diffeomorphism groups and homotopical properties of foliations, written for the Notices of the AMS.
We study families of singular holomorphic foliations on complex projective manifolds whose total intersection defines a foliation of unexpectedly low codimension.
Explicit representations of complex structures on closed manifolds are valuable, but relatively rare in the literature. Using isoparametric theory, we construct complex structures on isoparametric hypersurfaces with $g=4, m=1$ in the unit…
The notion of a linear deformation of a codimension one foliation into contact structures was introduced in [5]. This concept is a special type of deformation of confoliations. In this paper, we study linear deformations of pairs of…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
We exhibit isomorphisms of Grassmann spaces and their relationship with collineations and embeddings of the underlying projective spaces.
We study transnormal and isoparametric functions on closed Riemannian 4-manifolds and establish fundamental restrictions on their topology and geometry. In particular, we show that such manifolds cannot be endowed with negatively curved…
Associated with isoparametric foliations of unit spheres, there are two classes of minimal surfaces $-$ minimal isoparametric hypersurfaces and focal submanifolds. By virtue of their rich structures, we find new series of minimizing cones.…
We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.
In this note we use techniques in the topology of 2-complexes to recast some tools that have arisen in the study of planar tiling questions. With spherical pictures we show that the tile counting group associated to a set $T$ of tiles and a…
The notion of higher-order topological phases can have interesting generalizations to systems with subsystem symmetries that exhibit fractonic dynamics for charged excitations. In this work, we systematically study the higher-order…
We construct connections on $S^1$-equivariant Hamiltonian Floer cohomology, which differentiate with respect to certain formal parameters.