相关论文: Tangential LS-category of K(pi,1)-foliations

Associated with a smooth, $d$-closed $(1, 1)$-form $\alpha$ of possibly non-rational De Rham cohomology class on a compact complex manifold $X$ is a sequence of asymptotically holomorphic complex line bundles $L_k$ on $X$ equipped with $(0,…

We consider manifolds equipped with a foliation $\cal F$ of codimension $4q$, and an almost quaternionic structure $Q$ on the transversal bundle of ${\cal F}$. After discussing conditions of projectability and integrability of $Q$, we study…

We study deformation of spherical $CR$ circle bundles over Riemann surfaces of genus > 1. There is a one to one correspondence between such deformation space and the so-called universal Picard variety. Our differential-geometric proof of…

This paper examines the category C^k_{d,n} whose morphisms are d-dimensional smooth manifolds that are properly embedded in the product of a k-dimensional cube with an (d+n-k)-dimensional Euclidean space. There are k directions to compose…

We consider all complex projective manifolds X that satisfy at least one of the following three conditions: 1. There exists a pair $(C ,\varphi)$, where $C$ is a compact connected Riemann surface and $\varphi : C\to X$ a holomorphic map,…

Our main result is a generalization of Cappell's 5-dimensional splitting theorem. As an application, we analyze, up to internal s-cobordism, the smoothable splitting and fibering problems for certain 5-manifolds mapping to the circle. For…

For a singular Riemannian foliation whose leaves are properly embedded, we show in the first part of this article the existence of global tubular neighbourhoods, and we develop a global description of the foliation as stratification by…

We show that the K-theory cosheaf is a complete invariant for separable continuous fields with vanishing boundary maps over a finite-dimensional compact metrizable topological space whose fibers are stable Kirchberg algebras with rational…

We study totally geodesic codimension 1 smooth foliations on Lorentzian manifold. We are in particular interested by the relations between riemannian flows and geodesic foliations. We prove that, up to a 2-cover, any Seifert bundle admit…

Let F be a finitely generated discrete group. Given a covering map H to G of Lie groups with G either compact or complex reductive, there is an induced covering map Hom(F, H) to Hom(F, G). We show that when the fundamental group of G is…

In this article, we prove a series of integral formulae for a codimension-one foliated sub-Riemannian manifold, i.e., a Riemannian manifold $(M,g)$ equipped with a distribution ${\mathcal D}=T{\mathcal F}\oplus\,{\rm span}(N)$, where…

Moment-angle manifolds provide a wide class of examples of non-Kaehler compact complex manifolds. A complex moment-angle manifold Z is constructed via certain combinatorial data, called a complete simplicial fan. In the case of rational…

We study riemannian coverings $\varphi: \widetilde{M} \to \Gamma\backslash \widetilde{M}$ where $\widetilde{M}$ is a normal homogeneous space $G/K_1$ fibered over another normal homogeneous space $M = G/K$ and $K$ is locally isomorphic to a…

In this paper we study the fiber F of the rational Jones-Goodwillie character $$ F:=\hofiber(ch:K^\rat(A)@>>>HN^\rat(A)) $$ going from K-theory to negative cyclic homology of associative rings. We describe this fiber F in terms of sheaf…

The present paper unifies some aspects concerning the vertical Liouville distributions on the tangent (cotangent) bundle of a Finsler (Cartan) space in the context of generalized geometry. More exactly, we consider the big-tangent manifold…

We study the topology of the space of smooth codimension one foliations on a closed 3-manifold. We regard this space as the space of integrable plane fields included in the space of all smooth plane fields. It has been known since the late…

A notable example due to Heier, Lu, Wong, and Zheng shows that there exist compact complex K\"ahler manifolds with ample canonical line bundle such that the holomorphic sectional curvature is negative semi-definite and vanishes along…

We show that on a closed smooth manifold $M$ equipped with $k$ fiber bundle structures whose vertical distributions span the tangent bundle, every smooth diffeomorphism $f$ of $M$ sufficiently close to the identity can be written as a…

We investigate a new property for compact Kahler manifolds. Let X be a Kahler manifold of dimension n and let H^{1,1} denote the (1,1) part of its real second cohomology. On this space, we have an degree n form given by cup product. Let K…

On the slit tangent manifold of a Finsler manifold M are given the vertical and the Liouville foliations. In this paper we define some new types of vertical forms with respect to the Liouville foliation on TM^0. We define a cohomology group…