Related papers: Foliation adjunction

The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext…

We prove a cyclic Lefschetz formula for foliations. To this end, we define a notion of equivariant cyclic cohomology and show that its expected pairing with K-theory is well defined. This enables to associate to any invariant transverse…

We establish a form of 2-adjunction (tentatively termed the *fundamental 2-adjunction*), building on the fundamental adjunction proposed by Olivia Caramello and Riccardo Zanfa, which provides a constructive method for the associated stack…

Using a sums of squares formula for two variable polynomials with no zeros on the bidisk, we are able to give a new proof of a representation for distinguished varieties. For distinguished varieties with no singularities on the two-torus,…

This work deals with the topological classification of singular foliation germs on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and the…

We discuss residue formulae that localize the first Chern class of a line bundle to the singular locus of a given holomorphic connection. As an application, we explain a proof for Brunella's conjecture about exceptional minimal sets of…

We establish adjunction and inversion of adjunction for log canonical centers of arbitrary codimension in full generality.

The contents are divided into two papers "The Monotone Cumulants" (arXiv:0907.4896) and "Conditionally monotone independence" (arXiv:0907.5473).

A review is given of some recently obtained results on analytic contractions of Lie algebras and Lie groups and their applications to special function theory.

In this article, we prove the Sarkisov Program for co-rank one foliations with suitable singularities on normal projective threefolds. We also exibit a weaker version of birational super-rigidity between two foliated Mori fiber spaces with…

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…

We prove that, under mild restrictions, the space of codimension-one foliations of degree one on a smooth projective complete intersection has two irreducible components of logarithmic type. We also prove that the same conclusion holds for…

In this article, we show that for any deformation of analytic foliations, there exists a maximal analytic singular foliation on the space of parameters along the leaves of which the deformation is integrable.

The paper is devoted to the implicit function theorem involving singular mappings.We also discuss the form of the tangent cone to the solution set of the generalized equations in singular case and give some examples of applications to…

We derive a closed-form expression for the adjoint polynomials of torus knots and investigate their special properties. The results are presented in the very explicit double sum form and provide a deeper insight into the structure of…

These are slightly informal lecture notes intended for graduate students about the standard local theory of holomorphic foliations and vector fields. Though the material presented here is well-known some of the proofs differs slightly from…

We reduce the classification of finite extensions of function fields (of curves over finite fields) with the same class number to a finite computation; complete this computation in all cases except when both curves have base field…

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 develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…

We define Floer homology theories for oriented, singular knots in S^3 and show that one of these theories can be defined combinatorially for planar singular knots.