2 edition of **Stable maps of foliations in manifolds** found in the catalog.

Stable maps of foliations in manifolds

Mikhael Gromov

- 226 Want to read
- 13 Currently reading

Published
**1968**
by [s.n.] in [s.l.]
.

Written in English

**Edition Notes**

Statement | M.L. Gromov. |

ID Numbers | |
---|---|

Open Library | OL21369758M |

The author begins with motivations for the study of the subject and proceeds to discuss the instructive special case of transversally oriented foliations of codimension one. The second part of the book covers such topics as foliations by level hypersurfaces, infinitesimal automorphisms and basic forms, flows, Lie foliations, and twisted : The global study of foliations in the spirit of Poincare was begun only in the 's, by Ehresmann and Reeb. Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - Cited by:

If the manifold X is already foliated, one can use the construction to increase the codimension of the foliation, as long as f maps leaves to leaves. The Kronecker foliations of the 2-torus are the suspension foliations of the rotations R α: S 1 → S 1 by angle α ∈ [0, 2 π). Fe, has the same dimension as F; the two foliations Fe and F have the same local properties. Morphisms of foliations Let M and M0 be two manifolds endowed respec-tively with two foliations F and F0. A map f: M ¡! M0 will be called foliated or a morphism between F and F0 if, for every leaf L of F, f(L) is contained in a leafFile Size: KB.

This book includes surveys and research papers reflecting the broad spectrum of themes presented at the event. Of particular interest are the articles by F. Bonahon, “Geodesic Laminations on Surfaces”, and D. Gabai, “Three Lectures on Foliations and Laminations on 3-manifolds”, which are based on minicourses that took place during the. FOLIATIONS ON OVERTWISTED CONTACT MANIFOLDS 5 not covered there is the fact that the maps u: Σ˙ →M are not just injective but also embedded: for this one uses intersection theory to show that a critical point of uat z∈Σ implies intersections between (˙ a,u) and (a+ ǫ,u) near z for small ǫ; cf. [Wen]. Denote by PF ⊂M the union.

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Foliations and the geometry of 3-manifolds. This book gives an exposition of the so-called "pseudo-Anosov" theory of foliations of 3-manifolds, generalizing Thurston's theory of surface automorphisms. A central idea is that of a universal circle for taut foliations and other dynamical objects.

The idea of a universal circle is due to Thurston, although the development here differs in several technical points. STABLE MAPPINGS OF FOLIATIONS INTO MANIFOLDS M. GROMOV UDC Abstract. In this article we shall study the topological properties of sheaves of germs of map-pings, and for such sheaves construct an analog of obstruction theory.

The method proposed makesCited by: Request PDF | Stable mappings of foliations into manifolds | In this article we shall study the topological properties of sheaves of germs of mappings, Author: Mikhail Gromov.

Let (M′,F′) and (M,F) be two (compact or not) foliated manifolds, C ∞ F (M′, M) the space of smooth maps which send leaves into leaves. In this paper we prove that C ∞ F (M′, M) admits a structure of an infinite-dimensional manifold modeled on LF-spaces, provided that F is a Riemannian foliation or, more generally, when it admits an adapted local by: 1.

A smooth foliation is said to be transversely orientable if everywhere. [] 2 Special classes of foliations[] BundlesThe most trivial examples of foliations are products, foliated by the leaves.

(Another foliation Stable maps of foliations in manifolds book is given by.). A more general class are flat -bundles with or for a (smooth or topological) a representation, the flat -bundle with monodromy is given as.

The pseudo-Anosov theory of taut foliations. The purpose of this book is to give an exposition of the so-called “pseudo- Anosov”theory offoliations of theorygeneralizesThurston’s theory of surface automorphisms, and reveals an intimate connection between dynamics, geometry and topology in.

1 Introduction. Foliations of Riemannian manifolds can be considered as multidimensional dynamical systems: Riemannian structure (more precisely, Riemannian structure along the leaves) plays the role of time, the leaves play the role of orbits [Walczak].The dynamics of a foliation can be described in terms of its holonomy (see Foliations#Holonomy) pseudogroup.

STABILITY OF FOLIATIONS While this paper only deals with the stability of foliations in the neighborhood of a given compact leaf, i.e. stability in J x, Hirsch [HirschJ has dealt with the persistence of the compact leaf under perturbations.

Foliation germs at a compact manifold X; the basic homeomorphism theorem. Even if you are only interested in flows or diffeomorphisms, there are sometimes natural foliations associated to them. For instance, the stable/unstable foliations of an Anosov flow or diffeomorphism.

As for the mental picture of what a foliation is, well there are probably plenty of pictures online. of foliations on particular manifolds, and reported on examples and methods of construction of foliations due to wide variety of authors, including A’Campo [1], Alexander [8], Arraut [11], Durfee [, ], Fukui [], Lawson [,], Laudenbach [], Lickorish [], Moussu [, ].

Stable foliations. For some global bifurcations, reductions to homoclinic centre manifolds or other global centre manifolds are not possible.

In such situations, stable foliations may still provide reductions to semiflows on branched manifolds. This applies, in particular, to flows that contain Lorenz-like attractors, but also to studies of. [C02] L. Conlon, Foliations and locally free transformation groups of codimension two, Washington University, St.

Louis, Missouri (preprint). Zentralblatt MATH: Mathematical Reviews (MathSciNet): MR In [1] we proved that all harmonic foliations whose leaves are complex submanifolds on compact locally conformal Kähler manifolds are stable.

This is an analogue of the theorem " a holomorphic. Here the presence of singular submanifolds, corresponding to the singularities in the case of a dynamical system, is excluded.

This is the case we treat in this text, but it is by no means a comprehensive analysis. On the contrary, many situations in mathematical physics most definitely require singular foliations.

foliations, especially those of clagg C Example 1. Any manifold M can be foliated into pointÉ. That is, we let L be the unique O—dlmenelonal In spite of its manifold which maps bláectlvely to M. unprepossessing appearance, this pointwlse foliation WI 11 play File Size: 7MB.

Foliations of asymptotically ﬂat manifolds using constant mean curvature surfaces have been considered in [9], [24] and [6]. The uniqueness of such foliations was considered in [18]. In [9] these foliations have been used to deﬁne a center of mass for initial data sets for isolated gravitating systems in general relativity.

Stable and unstable manifolds. Stable and unstable manifolds of equilibrium points and periodic orbits are important objects in phase portraits. In physical systems subject to disturbances, the distance of a stable equilibrium point to the boundary of its stable manifold provides an estimate for the robustness of the equilibrium point.

From the Back Cover. The ideas and methods of foliations are very popular in mathematics and its applications. The key problem of this volume is the role of a Riemannian curvature in studies of manifolds and submanifolds with by: dational results in smooth manifold theory.

The concluding section leaves the reader with foliations and a brief look at their connection to the Frobenius theorem. 1 Preliminaries Let M be an m-dimensional manifold, TpM the tangent space to p ∈ M, and TM the tangent bundle of M.

Throughout this work, things are implicitly Size: KB. This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.

Index Theorems for Holomorphic Maps and Foliations Proposition Let Sbe a complex manifold. Then two exact sequences of locally free OS-modules are isomorphic if and only if they correspond to the same coho-mology class. In particular, an exact sequence () of. S. Hurder's lectures apply ideas from smooth dynamical systems to develop useful concepts in the study of foliations, like limit sets and cycles for leaves, leafwise geodesic flow, transverse exponents, stable manifolds, Pesin Theory, and hyperbolic, parabolic, and elliptic types of foliations, all of them illustrated with examples.FOLIATIONS ON SMOOTH MANIFOLDS Definition and Examples of Foliations Intuitively, a foliation corresponds to a decomposition of a manifold into a set of connected submanifolds of the seane dimension, called leaves, which locally look like the pages of a book.

Definition [].