Related papers: An invitation to singular foliations

This manuscript is an introduction to the theory of holomorphic foliations on the complex projective plane. Historically the subject has emerged from the theory of ODEs in the complex domain and various attempts to solve Hilbert's 16th…

Many mathematical models of physical phenomena that have been proposed in recent years require more general spaces than manifolds. When taking into account the symmetry group of the model, we get a reduced model on the (singular) orbit…

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 describe an approach to the issue of the singularities of null hypersurfaces, due to the focusing of null geodesics, in the context of the recently introduced formulation of GR via null foliations.

These lecture notes introduce conifold transitions between complex threefolds with trivial canonical bundle from the differential geometric point of view, and with a particular view towards aspects of mathematical physics and string theory.…

We build a germ of singular foliation in dimension two with analytical class of separatrix and holonomy representations prescribed. Thanks to this construction, we study the link between moduli of a foliation and moduli of its separatrix.

A smooth foliation is Riemannian when its leaves are locally equidistant. The closures of the leaves of a Riemannian foliation on a simply connected manifold, or more generally of a Killing foliation, are described by flows of transverse…

In this article, we describe the structure of codimension one foliations with canonical singularities and numerically trivial canonical class on varieties with terminal singularities, extending a result of Loray, Pereira and Touzet to this…

These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…

We construct families of non-trivial universal rigid secondary classes for foliations, and then discuss their application to prove that foliations are not homotopic. An observation of Lawson about the non-triviality of the normal Pontrjagin…

We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy…

These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Introduction. Lecture 1. WDVV equations and Frobenius manifolds. {Appendix A.} Polynomial…

A rather complete phenomenology of the singularities is developed according to a new algebraic point of view in the frame of Langlands global correspondences. That is to say,a process of: -singularizations and versal deformations of these,…

In these lectures notes I discuss the Linearization Theorem for Lie groupoids, and its relation to the various classical linearization theorems for submersions, foliations and group actions. In particular, I explain in some detail the…

We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these…

In this paper we study transversely holomorphic foliations of complex codimension one with some hypothesis on the transverse structure.

These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…

We study codimension one smooth foliations with Morse type singularities on closed ma-nifolds. We obtain a description of the manifold in case the number of centers in greater then the number of saddles. This result relies on and extends…

In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.

In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…