Related papers: Transverse LS-Category for Riemannian Foliations

The purpose of this article is to adapt the Frolicher-type inequality to the case of transversely holomorphic and transversely symplectic foliations. These inequalities can be used to e.g. determine whether a given foliation can be made…

In this paper we prove the conjecture of Molino that for every singular Riemannian foliation $(M,\mathcal{F})$, the partition $\bar{\mathcal{F}}$ given by the closures of the leaves of $\mathcal{F}$ is again a singular Riemannian foliation.

In this paper we survey on some recent results on Riemannian orbifolds and singular Riemannian foliations and combine them to conclude the existence of closed geodesics in the leaf space of some classes of singular Riemannian foliations…

We introduce and study the index morphism for G-invariant leafwise G-transversally elliptic operators on smooth closed foliated manifolds which are endowed with leafwise actions of the compact group G. We prove the usual axioms of excision,…

The $\pi_2$-diffeomorphism finiteness result (\cite{FR1,2}, \cite{PT}) asserts that the diffeomorphic types of compact $n$-manifolds $M$ with vanishing first and second homotopy groups can be bounded above in terms of $n$, and upper bounds…

We show that every co--orientable taut foliation F of an orientable, atoroidal 3-manifold admits a transverse essential lamination. If this transverse lamination is a foliation G, the pair F,G are the unstable and stable foliation…

Let G be a compact Lie group acting transitively on Riemannian manifolds M and N. Let p be a G equivariant Riemannian submersion from M to N. We show that a smooth differential form on N has finite Fourier series if and only if the pull…

For transversely homogeneous foliations on compact manifolds whose global holonomy group has connected closure, it is shown that either all holonomy covers of the leaves have polynomial growth with degree bounded by a common constant, or…

In this paper, we study the fundamental group of a certain class of globally hyperbolic Lorentzian manifolds with a positive curvature tensor. We prove that the fundamental group of lightlike geodesically complete parametrized Lorentzian…

In this paper we review some author's results about singular holonomy of singular riemannian foliations with sections (s.r.f.s for short) and also some results of a joint work with Toeben and a joint work with Gorodski. We stress here that…

We formulate and prove an analog of the Hopf Index Theorem for Riemannian foliations. We compute the basic Euler characteristic of a closed Riemannian manifold as a sum of indices of a non-degenerate basic vector field at critical leaf…

Consider a compact Riemannian manifold in dimension $n\geq 3$ with strictly convex boundary. We show that the transverse ray transform of $1$ tensors and the mixed ray transform of $1+1$ tensors are invertible, up to natural obstructions,…

A characteristic class for deformations of foliations called the Fuks-Lodder-Kotschick class (FLK class for short) is studied. It seems unknown if there is a real foliation with non-trivial FLK class. In this article, we show some…

We introduce a coarse analog of the classical Lusternik-Schnirelmann category which we denote by $\text{c-cat}$, defined for metric spaces in the coarse homotopy category. This provides a new tool for studying large-scale topological…

Let $M$ be a Riemannian manifold of dimension $n+1$ with smooth boundary and $p\in \partial M$. We prove that there exists a smooth foliation around $p$ whose leaves are submanifolds of dimension $n$, constant mean curvature and its arrive…

For a closed Riemannian manifold $M$ with a compact Lie group $G$ acting by isometries, we show that there are infinitely many $G$-invariant minimal hypersurfaces. Under the assumption that $M$ contains at most a finite number of minimal…

A singular riemannian foliation on a complete riemannian manifold is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. The singular foliation is said to admit…

We will show that any open Riemann surface $M$ of finite genus is biholomorphic to an open set of a compact Riemann surface. Moreover, we will introduce a quotient space of forms in $M$ that determines if $M$ has finite genus and also the…

Let $(M,g_M,\mathcal F)$ be a closed, connected Riemannian manifold with a Riemannian foliation $\mathcal F$ of nonzero constant transversal scalar curvature. When $M$ admits a transversal nonisometric conformal field, we find some…

A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a meager subset of the manifold.