Related papers: Foliations and diffeomorphism groups

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

In this work we relate the known results about the homotopy type of classifying spaces for smooth foliations, with the homology and cohomology of the discrete group of diffeomorphisms of a smooth compact connected oriented manifold. The…

Let (M,F) be a foliated manifold. We study the relationship between the basic cohomology Hb(M,F) of the foliation and the De Rham cohomology H(DF) of the space of leaves M/F as a quotient diffeological space. We prove that for an arbitrary…

This article is devoted to the geometric construction which states a natural correspondence between topological coverings of a foliated manifolds and noncommutative coverings of the operator algebras. However this correspondence is not one…

It is well-known that any isotopically connected diffeomorphism group $G$ of a manifold determines uniquely a singular foliation $\F_G$. A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism…

This is a brief overview of a few selected chapters on automorphism groups of affine varieties. It includes some open questions.

We interpret a formula for meromorphic functions on foliations by Riemann surfaces as an analogue to the product formula of valuations in algebraic number theory.

We study groups of formal diffeomorphisms in several complex variables. For abelian, metabelian or nilpotent groups we investigate the existence of suitable formal vector fields and closed differential forms which exhibit an invariance…

It is presented an example of a holomorphic foliation of a non-algebraizable surface which is topologically equivalent to an algebraic foliation.

We give a short, mostly elementary and self-contained proof of the classical result that the groups of diffeomorphisms, homeomorphisms, and homotopy equivalences of a surface have the same group of connected components.

This is a book on derived foliations, that are a generalisation of classical foliations in the context of derived geometry. The text starts with the basic definitions and constructions, then explore foliated cohomology (with crystal…

We study groups of formal or germs of analytic diffeomorphisms in several complex variables. Such groups are related to the study of the transverse structure and dynamics of Holomorphic foliations, via the notion of holonomy group of a leaf…

The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…

Let $\mathcal{F}$ be a Morse-Bott foliation on the solid torus $T=S^1\times D^2$ into $2$-tori parallel to the boundary and one singular central circle. Gluing two copies of $T$ by some diffeomorphism between their boundaries, one gets a…

This paper surveys recent results on classifying partially hyperbolic diffeomorphisms. This includes the construction of branching foliations and leaf conjugacies on three-dimensional manifolds with solvable fundamental group.…

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…

This essay summarizes the state of the art on some aspects of the dynamics of polynomial diffeomorphsms in complex dimension two, and it presents a number of open questions.

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…

This work focuses on the combinatorial properties of glued semigroups and provides its combinatorial characterization. Some classical results for affine glued semigroups are generalized and some methods to obtain glued semigroups are…

We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.