Related papers: The Gottschalk Conjecture

In this article, we study the geometric properties of codimension one foliations on Riemannian manifolds equipped with vector fields that are closed and conformal. Apart from its singularities, these vector fields define codimension one…

We prove that given two compact oriented $3$-manifolds $N$ and $M,$ with $M$ satisfying only a mild hypothesis, there is a hyperbolic $3$-manifold $N'$ arbitrarily ``closely related'' to $N,$ and such that $N'$ does not embed in $M.$ For…

Topology of Foliations of the Riemann Surfaces given by the real part of generic holomorphic 1-forms, is studied. Our approach is based on the notion of Transversal Canonical Basis of Cycles (TCB) instead of using just one closed…

A classic result due to Furstenberg is the strict ergodicity of the horocycle flow for a compact hyperbolic surface. Strict ergodicity is unique ergodicity with respect to a measure of full support, and therefore implies minimality. The…

It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P with the polygonal faces identified in…

We strengthen the unpublished theorem of Gabai and Mosher that every depth one sutured manifold contains a very full dynamic branched surface by showing that the branched surface can be chosen to satisfy an additional property we call…

A parallel lightlike vector field on a Lorentzian manifold $X$ naturally defines a foliation $\mathcal{F}$ of codimension one. If either all leaves of $\mathcal{F}$ are compact or $X$ itself is compact admitting a compact leaf and the…

The elliptic 3-manifolds are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, that is, those that have finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic…

We prove that every plane passing through the origin divides an embedded compact free boundary minimal surface of the euclidean $3$-ball in exactly two connected surfaces. We also show that if a region in the ball has mean convex boundary…

We describe transversely oriented foliations of codimension one on closed manifolds that admit simple foliated flows.

The main theorem states that any complete connected Riemannian manifold of bounded geometry can be isometrically realized as a leaf with trivial holonomy in a compact Riemannian foliated space.

We say that a topological $n$-manifold $N$ is a cubical $n$-manifold if it is contained in the $n$-skeleton of the canonical cubulation $\mathcal{C}$ of ${\mathbb{R}}^{n+k}$ ($k\geq1$). In this paper, we prove that any closed, oriented…

In this short note, we study the injectivity radius bound for three dimensional complete and non-compact Riemannian manifold with good leaf foliations and with bounded curvature up to first order. We obtain the injectivity bound by using…

Let $M_1$ and $M_2$ be knot manifolds and $M=M_1\cup_f M_2$ be the closed 3-manifold obtained by gluing up $M_1$ and $M_2$ via $f:\partial M_1\xrightarrow{\cong} \partial M_2$. We show that if $M$ admits a co-oriented taut foliation, then…

We present existence results for certain singular 2-dimensional foliations on 4-manifolds. The singularities can be chosen to be simple, e.g. the same as those that appear in Lefschetz pencils. There seems to be a wealth of such creatures…

In the first part of this paper we will prove the Voevodsky's nilpotence conjecture for smooth cubic fourfolds and ordinary generic Gushel-Mukai fourfolds. Then, making use of noncommutative motives, we will prove the Voevodsky's nilpotence…

We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that states that low degree cohomology classes of arithmetic manifolds of orthogonal…

An orbit-like foliation is a singular foliation on a complete Riemannian manifold $M$ whose leaves are locally equidistant (i.e., a singular Riemannian foliation) and (transversely) infinitesimally homogenous. This class of singular…

A homeomorphism f of a manifold M is called H_1-transitive if there is a transitive lift of an iterate of f to the universal Abelian cover \tM. Roughly speaking, this means that f has orbits which repeatedly and densely explore all elements…

This paper explores the conjecture that the following are equivalent for rational homology 3-spheres: having left-orderable fundamental group, having non-minimal Heegaard Floer homology, and admitting a co-orientable taut foliation. In…