Related papers: Isoparametric foliations, diffeomorphism groups an…

We prove that the open unit ball $\mathbb{B}_n$ of $\mathbb{C}^n$ $(n\ge 2)$ admits a nonsingular holomorphic foliation $\mathcal F$ by closed complex hypersurfaces such that both the union of the complete leaves of $\mathcal F$ and the…

This note serves to record examples of diffeomorphisms of closed smooth $4$-manifolds $X$ that are homotopic but not pseudoisotopic to the identity, and to explain why there are no such examples when $X$ is orientable and its fundamental…

We prove that in dimensions not equal to 4, 5, or 7, the homology and homotopy groups of the classifying space of the topological group of diffeomorphisms of a disk fixing the boundary are finitely generated in each degree. The proof uses…

This article describes the geometry of isomorphisms between complements of geometrically irreducible closed curves in the affine plane $\mathbb{A}^2$, over an arbitrary field, which do not extend to an automorphism of $\mathbb{A}^2$. We…

We investigate the local geometry of a pair of independent contact structures on 3-manifolds under maps that independently preserve each contact structure. We discover that such maps are homotheties on the contact 1-forms and we discover…

We introduce the $2$-nodal spherical deformation of certain singular fibers of genus $2$ fibrations, and use such deformations to construct various examples of simply connected minimal symplectic $4$-manifolds with small topology. More…

In this article, we focus on a very special class of foliations with complex leaves whose diffeomorphism type is fixed. They have a unique compact leaf and the noncompact leaves all accumulate onto it. We show that the complex structure…

The $\theta$-deformed Hopf fibration $\mathbb{S}^3_\theta\to \mathbb{S}^2$ over the commutative $2$-sphere is compared with its classical counterpart. It is shown that there exists a natural isomorphism between the corresponding associated…

We describe the space of measured foliations induced on a compact Riemann surface by meromorphic quadratic differentials. We prove that any such foliation is realized by a unique such differential $q$ if we prescribe, in addition, the…

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…

Let $\mathcal{G}$ be a Morse-Bott foliation on the solid Klein bottle $\mathbf{K}$ into $2$-dimensional Klein bottles parallel to the boundary and one singular circle $S^1$. Let also $S^1\widetilde{\times}S^2$ be the twisted bundle over…

We determine the structure of the fundamental group of the regular leaves of a closed singular Riemannian foliation on a compact, simply connected Riemannian manifold. We also study closed singular Riemannian foliations whose leaves are…

We use surgery along 2-tori embedded in a union of two copies of a product of punctured 2-tori to produce a new collection of homotopy 4-spheres (4-manifolds homotopy equivalent to $S^4$ and hence homeomorphic to $S^4$ but possibly not…

A meromorphic quadratic differential on a punctured Riemann surface induces horizontal and vertical measured foliations with pole-singularities. In a neighborhood of a pole such a foliation comprises foliated strips and half-planes, and its…

Given a finite group action on a smooth manifold, we study the following question: if two equivariant diffeomorphisms are isotopic, must they be equivariantly isotopic? Birman-Hilden and Maclachlan-Harvey proved the answer is "yes" for most…

A fibration of a Riemannian manifold is fiberwise homogeneous if there are isometries of the manifold onto itself, taking any given fiber to any other one, and preserving fibers. Examples are fibrations of Euclidean n-space by parallel…

In this paper, we establish a number of results about the topology of the leaves of a closed singular Riemannian foliation $(M,\fol)$. If $M$ is simply connected, we prove that the leaves are finitely covered by nilpotent spaces, and…

A U(n)-manifold is multiaxial if the isotropy groups are always conjugate to unitary subgroups. The classification and the concordance of such manifolds have been studied by Davis, Hsiang and Morgan under much more strict conditions. We…

Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…

The present paper is a continuation of [13], [14] of the authors. Specifically, the paper considers the MD5-foliations associated to connected and simply connected MD5-groups such that their Lie algebras have 4-dimensional commutative…