Related papers: Derived Foliations
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
The theories of strings and $D$-branes have motivated the development of non Abelian cohomology techniques in differential geometry, on the purpose to find a geometric interpretation of characteristic classes. The spaces studied here, like…
A singular foliation is a partition of a manifold into leaves of perhaps varying dimension. Stefan and Sussmann carried out fundamental work on singular foliations in the 1970s. We survey their contributions, show how diffeological objects…
We discuss various problems regarding the structure of the foliation of some foliated submanifolds S of C^n, in particular Levi flat ones. As a general scheme, we suppose that S is bounded along a coordinate (or a subset of coordinates),…
This is a survey concerning the relationship between Lie Groupoids (and their morphisms) and singular foliations in the sense of Sussmann-Stefan (considered from a purely geometrical point of view). We focus on the interaction between the…
We describe notions of tautness that arise in the study of $C^0$ foliations, $C^{1,0}$ or smoother foliations, and in geometry. We give examples to show that these notions are different, and discuss how these differences impact some…
This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the…
Starting from the axiomatic description of meromorphic functions with prescribed analytic properties, we introduce the cosimplicial cohomology of restricted meromorphic functions defined on foliations of smooth complex manifolds. Spaces for…
Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type…
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…
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and…
We formalize the concepts of holomorphic affine and projective structures along the leaves of holomorphic foliations by curves on complex manifolds. We show that many foliations admit such structures, we provide local normal forms for them…
Continuing the study of bounded geometry for Riemannian foliations, begun by Sanguiao, we introduce a chart-free definition of this concept. Our main theorem states that it is equivalent to a condition involving certain normal foliation…
We study holomorphic foliations with an affine homogeneous transverse structure. We give a friendly characterization of the case of transversely affine foliations in terms of matrix valued pairs of differential forms. This leads naturally…
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…
This is a survey paper dealing with holomorphic G-structures and holomorphic Cartan geometries on compact complex manifolds. Our emphasis is on the foliated case: holomorphic foliations with transverse (branched or generalized) holomorphic…
This paper introduces a new type of open book decomposition for a contact three-manifold with a specified characteristic foliation $\mathcal{F}_\xi$ on its boundary. These \textit{foliated open books} offer a finer tool for studying contact…
We discuss a relation between the structure of derived categories of smooth projective varieties and their birational properties. We suggest a possible definition of a birational invariant, the derived category analogue of the intermediate…
We produce examples of codimension one foliations of the Euclidean and hyperbolic planes with bounded geometry which are topologically products, but for which leaves are non-recursively distorted. That is, the function which compares…
We develop a unified framework for the study of properties involving diagonalizations of dense families in topological spaces. We provide complete classification of these properties. Our classification draws upon a large number of methods…