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

Stable maps of foliations in manifolds

Mikhael Gromov

- 363 Want to read
- 39 Currently reading

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

Written in English

**Edition Notes**

Statement | M.L. Gromov. |

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

Open Library | OL21369758M |

Examples include hyperbolic 3-manifolds of every possible homological type. We show that all such foliations admit transverse pseudo-Anosov flows, and that in the universal cover of the hyperbolic cases, the leaves limit to sphere-filling Peano curves. The skew R-covered Anosov foliations . Foliations: The collection of local stable/unstable manifolds for the geodesic flow on a compact manifold of strictly negative curvature. The same for an Anosov diffeomorphism or Axiom A diffeomorphism. For example, the holonomies of a strong stable foliation inside the stable . An algebraic foliation chart for a foliated manifold is a foliation chart for which the transition maps are polynomial maps. What is an example of an analytic foliation of the Euclidean space $\ ential-geometry cal-systems foliations.

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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 Stable maps of foliations in manifolds book 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 of 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 Stable maps of foliations in manifolds book to give an exposition of the so-called “pseudo- Anosov”theory offoliations of theorygeneralizesThurston’s theory of surface automorphisms, and reveals Stable maps of foliations in manifolds book 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 Stable maps of foliations in manifolds book 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 Stable maps of foliations in manifolds book 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 Stable maps of foliations in manifolds book 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 []. This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows 5/5(6).

This book provides historical background and a complete overview of the qualitative theory of foliations and differential dynamical systems. Senior mathematics majors and graduate students with background in multivariate calculus, algebraic and differential topology, differential geometry, and linear algebra will find this book an accessible introduction.

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. Foliations exist for generic contact forms on the tight three-sphere. Corollary.2 or 1. Theorem (Abbas ’04).Giroux’s open book decompositions in the planar case can be de-formed into spherical nite energy foliations.

Corollary (Abbas, Cieliebak, Hofer ’04).We-instein conjecture for planar contact struc-tures. on an -dimensional manifold.

A decomposition of into path-connected subsets, called leaves, such that can be covered by coordinate neighbourhoods with local coordinates, in terms of which the local leaves, that is, the connected components of the intersection of the leaves with, are given by the equations.A foliation in this sense is called a topological foliation.

This book brings selected works presented at the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities and Foliations.

Geometry, Topology and Applications BMMS 2/NBMS 3, Salvador, Brazil, Singular Fibers of Stable Maps of Manifold Pairs and Their Applications. Pages Saeki. of transverse knots in contact manifolds.

Foliations and distributions on 4-manifolds The question of whether a given manifold admits a foliation of a given dimension is a very di cult one in general.

An obvious necessary condition for the existence of a q-dimensional foliation is the existence of a q-dimensional distribution. Foliated CR manifolds DRAGOMIR, Sorin and NISHIKAWA, Seiki, Journal of the Mathematical Society of Japan, ; Alexander-Spanier cohomology of foliated manifolds Masa, Xosé M., Illinois Journal of Mathematics, ; Affine Hirsch foliations on $3$–manifolds Yu, Bin, Algebraic & Geometric Topology, ; Topological canal foliations HECTOR, Gilbert, LANGEVIN, Rémi, and WALCZAK, Paweł Cited by: We announce some results towards the classification of partially hyperbolic diffeomorphisms on 3-manifolds, and outline the proofs in the case when the diffeomorphism is dynamically coherent.

Detailed proofs are long and technical and will appear later. Buy Foliations and the Geometry of 3-Manifolds (Oxford Mathematical Monographs) by Calegari, Danny (ISBN: ) from Amazon's Book Store.

Everyday low prices and free delivery on eligible : Danny Calegari. paper giving a construction for foliations of 3-manifolds which is similar to, but simpler than, the methods of this paper. For the last two sections, which deal with homotopy classes of Haefliger structures, Thurston [24] is a prerequisite.

THEOREM 1. (a) A closed manifold Mn has a C- codimension-one foli. Riemannian foliations on contractible manifolds Luis Florit, Oliver Goertsches, Alexander Lytchak, and Dirk To¨ben (CommunicatedbyBurkhardWilking) Abstract.

We prove that Riemannian foliations on complete contractible manifolds have a closed leaf, and that all leaves are closed if one closed leaf has a ﬁnitely generated fundamental Size: KB. a center unstable manifold. For each small translation we prove the existence of pdf stable manifold containing the translated front and show that the stable manifolds foliate a small ball centered at the front.

1. Introduction Traveling fronts are solutions to partial di erential equations which move with.Thus, the existence was established of a closed leaf in any two-dimensional smooth foliation on many three-dimensional manifolds (e.g.

spheres). Several results in the qualitative theory of foliations were intended to clarify the problem of the existence of an important class of hyperbolic dynamical systems on manifolds.- Foliations of underlying ebook structures (e.g.

Poisson, Dirac) - Geometric control theory, with holonomic and non-holonomic constraints: foliation by accessible sets - Etc. (Background picture: Stable and unstable foliations of a hyperbolic geodesic ow) Nguyen Tien Zung (IMT) Lectures on Singular Foliations Sanya /March/ 4 /