Foliations : Geometry and Dynamics - Proceedings of the Euroworkshop.
Title:
Foliations : Geometry and Dynamics - Proceedings of the Euroworkshop.
Author:
Walczak, Pawel.
ISBN:
9789812778246
Personal Author:
Physical Description:
1 online resource (462 pages)
Contents:
CONTENTS -- SURVEY ARTICLES -- Some results on secondary characteristic classes of transversely holomorphic foliations -- 1 Introduction -- 2 Examples -- 3 Definitions -- 4 Rigidity and residuality -- 5 Another relation between the Bott class and the Godbillon-Vey class -- References -- LS-categories for foliated manifolds -- 1 Introduction -- 2 LS-category -- 3 Fibrewise category -- 4 Equivariant category -- 5 Foliated categories -- References -- Dynamics and the Godbillon-Vey class: a history and survey -- 1 A simple definition -- 2 Structure theory -- 3 Duminy's Theorem -- 4 Ergodic theory -- 5 Geometric entropy -- 6 Exceptional minimal sets -- 7 Extensions of Godbillon-Vey -- 8 Tricks and treats -- 9 Open questions -- References -- Similarity and conformal geometry of foliations -- 1 Euclidean integral geometry for foliations -- 2 Dimension-one foliations of homothety surfaces -- 3 The set of spheres -- 4 Codimension-one foliation of R³, S³ or H³ -- 5 Bilocal statements -- References -- Foliations and contact structures on 3-manifolds -- 0 Introduction to contact geometry -- 1 3D contact topology due to Bennequin -- 2 Fillable contact structures and tightness -- 3 Contact structures and foliations: focused on the theory of confoliations -- 4 Anosov flows and bi-contact structures -- 5 Problems -- References -- Operator algebras and the index theorem on foliated manifolds -- Introduction -- 1 Topology of the leaf space M/F -- 2 Analysis on the leaf space M/F -- 3 Toward noncommutative geometry on foliated manifolds -- References -- RESEARCH PAPERS -- Distributional Betti numbers of transitive foliations of codimension one -- 1 Introduction -- 2 Distributional Betti numbers -- 3 The distributional Euler characteristic and functions of the leafwise Laplacian.
4 Distributional Euler characteristic and Connes' Euler characteristic -- 5 Localization theorem -- 6 The Lefschetz trace formula -- References -- Circle at infinity influences on the smoothness of surface flows -- Introduction -- 1 Preliminaries -- 2 Proof of the main theorem -- References -- Entropies of hyperbolic groups and some foliated spaces -- 1 Introduction -- 2 Entropy -- 3 Growth -- 4 Hyperbolic spaces and groups -- 5 Proof of the Theorem -- 6 Suspensions -- References -- Tautly foliated 3-manifolds with no R-covered foliations -- 1 Introduction -- 2 R-covered almost implies taut -- 3 Taut but not R-covered -- 4 R-covered finite covers -- 5 Concluding remarks -- References -- Endsets of exceptional leaves -- a theorem of G. Duminy -- 1 Duminy's theorems -- 2 The proof of Theorem 1.1 and Theorem 1.4 -- 3 Unbounded holonomy -- 4 Some derivative estimates -- 5 In the absence of a contraction -- 6 Existence of the contraction -- 7 A compactly supported cohomology class -- 8 Problems -- 9 Examples of Markov minimal sets -- References -- Some remarks on partially holomorphic foliations -- 1 Linear algebraic background -- 2 Bundle structures and Bott connection -- 3 Formal integrability and main results -- References -- Foliations and compactly generated pseudogroups -- 1 Compactly generated pseudogroups -- 2 Pseudogroups of holomorphic transformations of a complex curve -- 3 The fundamental groupoid and compact presentation -- References -- Traces and invariants for non-compact manifolds -- 1 Introduction -- 2 Haefliger functions and the trace -- 3 Dirac complexes and Lefschetz functions -- 4 Fixed point indices and the Lefschetz theorem -- 5 An example -- 6 Proof of Lefschetz theorem -- 7 Functionals on Ch(M) -- References -- Hilbert modules of foliated manifolds with boundary -- 1 Introduction -- 2 Preliminaries.
3 Partitioned and boundary modules -- 4 Callias type operators -- 5 Bordism of foliations -- 6 Foliation with longitudinal positive scalar curvature -- 7 Example: the smooth case -- References -- Non-Euclidean affine laminations -- 1 Affine and hyperbolic laminations -- 2 Foliations and laminations associated 'with the hyperbolic space -- 3 An example of a non-Euclidean affine foliation -- References -- Transverse Lusternik-Schnirelmann category and non-proper leaves -- References -- Structurally stable diffeomorphisms have no codimension one Plykin attractors on 3-manifolds -- Introduction -- 1 Main definitions -- 2 Preliminaries -- 3 Proof of the main theorem -- References -- On exact Poisson manifolds of dimension 3 -- 1 Introduction -- 2 Generalized divergence and the Schouten bracket -- 3 Exact Poisson manifolds of special kind -- 4 Exact Poisson structures on closed manifolds -- 5 A construction of exact Poisson manifolds -- References -- Foliation cones corresponding to some pretzel links -- 1 Introduction -- 2 Computing examples -- 3 Proof of main theorem -- References -- Regular projectively Anosov flows without compact leaves -- 1 Introduction and the statement of the result -- 2 Induced flow and foliations in the universal covering -- 3 Proof of Theorem 1.1 -- 4 Proof of Theorem 1.2 -- 5 Asymptotic cycles -- References -- On the perfectness of groups of diffeomorphisms of the interval tangent to the identity at the endpoints -- 1 Introduction -- 2 Perfectness of the group of homeomorphisms of the closed interval -- 3 Perfectness of the group of Lipschitz homeomorphisms of the closed interval.
4 Perfectness of the group of the C1 diffeomorphisms of the closed interval which are tangent to the identity at the endpoints -- 5 Perfectness of the group of the Coo diffeomorphisms of the closed interval which are infinitely tangent to the identity at the endpoints -- 6 Appendix. Small commutators of C1 diffeomorphisms -- References -- Basic distribution for singular Riemannian foliations -- 1 The case of regular Riemannian foliations -- 2 Basic functions -- 3 The case of singular Riemannian foliations -- References -- List of participants -- Program.
Abstract:
This volume contains surveys and research articles regarding different aspects of the theory of foliation. The main aspects concern the topology of foliations of low-dimensional manifolds, the geometry of foliated Riemannian manifolds and the dynamical properties of foliations. Among the surveys are lecture notes devoted to the analysis of some operator algebras on foliated manifolds and the theory of confoliations (objects defined recently by W Thurston and Y Eliashberg, situated between foliations and contact structures). Among the research articles one can find a detailed proof of an unpublished theorem (due to Duminy) concerning ends of leaves in exceptional minimal sets. Contents: Survey Articles:: Some Results on Secondary Characteristic Classes of Transversely Holomorphic Foliations (T Asuke); LS-Categories for Foliated Manifolds (H Colman); Dynamics and the Godbillon-Vey Class: A History and Survey (S Hurder); Similarity and Conformal Geometry of Foliations (R Langevin); Foliations and Contact Structures on 3-Manifolds (Y Mitsumatsu); Operator Algebras and the Index Theorem on Foliated Manifolds (H Moriyoshi); Research Articles:: Distributional Betti Numbers of Transitive Foliations of Codimension One (J Álvarez-López & Y Kordyukov); Tautly Foliated 3-Manifolds with No R-Covered Foliations (M Brittenham); Endests of Exceptional Leaves - A Theorem of G Duminy (J Cantwell & L Conlon); Foliations and Compactly Generated Pseudogroups (A Haefliger); Transverse Lusternik-Schnirelmann Category and Non-Proper Leaves (R Langevin & P Walczak); On Exact Poisson Manifolds of Dimension 3 (T Mizutani); On the Perfectness of Groups of Diffeomorphisms of the Interval Tangent to the Identity at the Endpoints (T Tsuboi); and other papers. Readership: Researchers interested in mathematics, especially in fields related to differential geometry and topology,
and the theory of dynamical systems.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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