Related papers: Foliations on the open $3$-ball by complete surfac…

Let F be a foliation in a closed 3-manifold with negatively curved fundamental group and suppose that F is almost transverse to a quasigeodesic pseudo-Anosov flow. We show that the leaves of the foliation in the universal cover extend…

In this work, we find an equation that relates the Ricci curvature of a riemannian manifold $M$ and the second fundamental forms of two orthogonal foliations of complementary dimensions, $\mathcal{F}$ and $\mathcal{F}^{\bot}$, defined on…

For a closed manifold $M$, let Fib$(M)$ be the number of distinct fiberings of $M$ as a fiber bundle with fiber a closed surface. In this paper we give the first computation of Fib$(M)$ where $1<\text{Fib}(M)<\infty$ but $M$ is not a…

We study smooth foliations of arbitrary codimension on homogeneous compact K\"ahler manifolds. We prove that smooth foliations on rational compact homogeneous manifolds are locally trivial fibrations and classify the smooth foliations with…

We consider foliations of compact complex manifolds by analytic curves. We suppose that the line bundle tangent to the foliation is negative. We show that in a generic case there exists a finitely smooth homeomophism, holomorphic on the…

This is an example on the cohomology of threefolds.

Let $M$ be a closed hyperbolic 3-manifold with a fibered face $\sigma$ of the unit ball of the Thurston norm on $H_2(M)$. If $M$ satisfies a certain condition related to Agol's veering triangulations, we construct a taut branched surface in…

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

We study Riemannian foliations with complex leaves on Kaehler manifolds. The tensor T, the obstruction to the foliation be totally geodesic, is interpreted as a holomorphic section of a certain vector bundle. This enables us to give…

If $(M^n, g)$ is a closed Riemannian manifold where every unit ball has volume at most $\epsilon_n$ (a sufficiently small constant), then the $(n-1)$-dimensional Uryson width of $(M^n, g)$ is at most 1.

We show that the absolute period foliation of the principal stratum of abelian differentials on a surface of genus at least 3 is ergodic. We also investigate the absolute period foliation of affine invariant manifolds.

The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate…

This thesis is concerned with equidistant foliations of Euclidean space, i.e. partitions into complete, connected, properly embedded smooth submanifolds. The space of leaves is an Alexandrov space of nonnegative curvature and the canonical…

A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…

For a closed orientable irreducible $3$-manifold $M$ that admits a co-orientable taut foliation with one-sided branching, we show that $\pi_1(M)$ is left orderable.

A foliation F on a Riemannian manifold M is homogeneous if its leaves coincide with the orbits of an isometric action on M. A foliation F is polar if it admits a section, that is, a connected closed totally geodesic submanifold of M which…

In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is…

We answer the question of when the underlying space of an orbifold is a manifold with boundary in several categories.

We consider a compact manifold $(M,\mathfrak{F})$ with a foliation $\mathfrak{F}$, and a smooth affine connection $\nabla$ on the tangent bundle of the foliation $T\mathfrak{F}$. We introduce and study a foliated completeness problem.…

We show that the integral foliated simplicial volume of a connected compact oriented smooth manifold with a regular foliation by circles vanishes.