Foliations 2005 : Proceedings of the International Conference.
Title:
Foliations 2005 : Proceedings of the International Conference.
Author:
Walczak, Pawel.
ISBN:
9789812772640
Personal Author:
Physical Description:
1 online resource (488 pages)
Contents:
CONTENTS -- Preface -- Morphisms of pseudogroups and foliated maps -- 1 Introduction -- 2 Morphisms of pseudogroups -- 3 Holonomy pseudogroups of foliated spaces -- 4 Holonomy morphisms of foliated maps -- 5 Leafwise homotopies and foliated homotopies -- 6 Complete pseudogroups and complete morphisms -- 7 Pseudogroups of local isometries -- 8 Riemannian foliations -- 9 Morphisms of complete pseudogroups of local isometries -- 10 Ideas of the proof of Proposition 9.2 -- 11 Smoothness along the orbit closures -- 12 The strong plaquewise topology -- 13 Smooth approximation for Riemannian foliations -- 14 The spectral sequence of a Coo foliation -- 15 Foliated homotopy invariance of the spectral sequence -- 16 Examples -- 17 Open problems -- References -- Codimension-one foliations with a transversely contracting flow -- 1 Introduction -- 2 Preliminaries -- 3 Flows with invariant foliations -- References -- On infinitesimal derivatives of the Bott class -- 1 Introduction -- 2 Relationship of infinitesimal derivatives of the Bott class and the Schwarzian derivatives -- 3 Some applications -- References -- Dense orbits for abelian subgroups of GL(n C) -- 1 Introduction -- 2 Matrix normal forms -- 3 Matrix exponential map -- 4 Some properties of subgroups of K*nr(C) -- 5 Parametrization -- 6 Dense orbit for subgroups of K*nr(C) -- 7 Proofs of main theorems -- 8 Finitely generated subgroups -- References -- Hirsch foliations in codimension greater than one -- 1 Introduction -- 2 Hirsch foliations in codimension one -- 3 Systems of etale correspondences -- 4 Generalized Hirsch foliations -- 5 Realizing systems of etale correspondences -- 6 Examples -- 7 Some Questions -- References -- Extrinsic geometry of foliations on 3-manifolds -- 1 Introduction -- 2 Classes of foliations -- 3 Basic problems.
4 Topological obstructions -- 5 Duality -- 6 Trick -- 7 Examples of strong saddle foliations -- 8 Strong saddle foliation on S3 -- References -- Classification of Morse-Smale diffeomorphisms with the chain of saddles on 3-manifolds -- 1 Introduction -- 2 The proof of Theorem 1 -- 3 Cut and squeeze operations on the manifold N = S2 x S1 -- 4 Dynamics of a diffeomorphism f E Gn -- 5 The proof of Theorem 2 -- 6 The proof of Theorem 3 -- 7 Sketch of the proof for Theorem 4 -- References -- Extrinsic geometry of foliations -- Introduction -- 1 Totally and almost totally geodesic foliations -- 2 Minimal and CMC foliations -- 3 Total umbilicity -- 4 Dupin foliations and some generalizations -- 5 Final comments -- References -- Surface dynamical systems and foliations via geodesic laminations -- 1 Introduction -- 2 Main definitions -- 3 Topological classification -- 4 Topological conjugacy -- 5 Deviations -- 6 Dynamics and absolute -- 7 Absolute and smoothness -- 8 On continuity and collapse of geodesic frameworks -- References -- On rigidity of submanifolds tangent to nonintegrable distributions -- 1 Introduction -- 2 Basic definitions -- 3 Rigidity -- 4 Rigidity of submanifolds without boundary -- 5 Engel distributions -- 6 Accessible sets -- 7 Non-rigidity in Engel distributions -- References -- Transversal twistor spinors on a Riemannian foliation -- 1 Introduction -- 2 Preliminaries and known facts -- 3 Transversal twistor spinors -- 4 Transversal Killing spinors -- 5 The conformal relationship between transversal twistor spinors and transversal Killing spinors -- 6 The transversal Weyl conformal curvature tensor -- References -- A Birkhhoff section for the Bonatti-Langevin example of Anosov flow -- 1 Introduction -- 2 The Bonatti-Langevin example -- 3 Birkhoff section and the return map.
4 Braid representation and Generalization -- References -- A remark on a relation between foliations and number theory -- References -- Noncommutative spectral geometry of Riemannian foliations: Some results and open problems -- Introduction -- 1 Preliminaries on pseudodifferential operators -- 2 Some noncommutative spaces associated with the leaf space -- 3 Transverse pseudodifferential calculus -- 4 Transverse dynamics -- 5 Transverse Riemannian geometry -- References -- A survey on simplicial volume and invariants of foliations and laminations -- 1 Volume and Topology -- 2 Foliations and Laminations -- 3 Invariants of foliations and laminations -- References -- Harmonic foliations of the plane a conformal approach -- 1 The moving frame method -- 2 Harmonic foliations of a sphere or of a flat torus -- 3 The set of oriented circles of S2 -- 4 Local and bilocal invariants. -- References -- Consecutive shifts along orbits of vector fields -- 1 Introduction -- 2 Characteristic polynomials of products of two matrices -- 3 Shifts that are diffeomorphisms -- 4 Representation of a leaf-preserving mapping as a shift -- 5 Acknowledgements -- References -- A Lie algebroid and a Dirac structure associated to an almost Dirac structure -- 1 Introduction -- 2 Courant algebroid of a Lie algebroid -- 3 Computation of the kernel of T -- 4 Presymplectic structure of Co -- 5 Jacobi Structure and an example -- References -- Convergence of contact structures to foliations -- 1 Introduction -- 2 Convergence along Vector Field -- 3 Thurston's and Thurston-Bennequin's Inequalities -- 4 Anosov and Projectively Anosov Flows -- 5 Spinnable Structures -- References -- Generalized equivariant index theory -- 1 Introduction -- 2 The Atiyah-Singer Index Theorem -- 3 Equivariant Index Theory -- 4 Manifolds with Boundary.
5 New Results in Equivariant Index Theory -- 6 Foliation-Equivariant Index Theory -- References -- Vanishing results for spectral terms of a Riemannian foliation -- 1 Introduction -- 2 Levi-Civita connection and adiabatic limits -- 3 Curvature tensor and adiabatic limits -- 4 Weitzenbock formula and adiabatic limits -- 5 Vanishing conditions for the spectral sequence of a Riemannian foliation -- References -- The generalized Weyl group of a singular Riemannian foliation -- 1 Overview -- 2 The transversal holonomy group T -- 3 Applications -- References -- On the group of foliation preserving diffeomorphisms -- 1 Introduction and the statement of the result -- 2 Fragmentation -- 3 Cocycles for DiffF(M) -- References -- Conformally defined geometry on foliated Riemannian manifolds -- Introduction -- 1 Conformal metric and volume -- 2 Intrinsic geometry -- 3 Extrinsic geometry -- 4 An integral formula -- 5 Final remarks -- References -- Problem Set -- 1 Introduction -- 2 Ergodic theory and dynamics -- 3 Minimal sets -- 4 Group actions -- 5 Holomorphic foliations -- 6 Topology of foliations -- 7 Harmonic measures -- 8 Geometry of foliations -- 9 (Singular) Riemannian foliations -- 10 Godbillon-Vey classes -- References -- List of participants -- Program.
Abstract:
This volume takes a look at the current state of the theory of foliations, with surveys and research articles concerning different aspects. The focused aspects cover geometry of foliated Riemannian manifolds, Riemannian foliations and dynamical properties of foliations and some aspects of classical dynamics related to the field. Among the articles readers may find a study of foliations which admit a transverse contractive flow, an extensive survey on non-commutative geometry of Riemannian foliations, an article on contact structures converging to foliations, as well as a few articles on conformal geometry of foliations. This volume also contains a list of open problems in foliation theory which were collected from the participants of the Foliations 2005 conference. Sample Chapter(s). Chapter 1: Morphisms of Pseudogroups and foliated Maps (808 KB). Contents: Morphisms of Pseudogroups and Foliated Maps (J Álvarez López & X Masa); On Infinitesimal Derivatives of the Bott Class (T Asuke); Hirsch Foliations in Codimension Greater Than One (A Bis, S Hurder & J Shive); Extrinsic Geometry of Foliations on 3-Manifolds (D Bolotov); Extrinsic Geometry of Foliations (M Czarnecki & P Walczak); Transversal Twistor Spinors on a Riemannian Foliation (S D Jung); A Survey on Simplicial Volume and Invariants of Foliations and Laminations (T Kuessner); Harmonic Foliations of the Plane, a Conformal Approach (R Langevin); Consecutive Shifts Along Orbits of Vector Fields (S Maksymenko); Generalized Equivariant Index Theory (K Richardson); Vanishing Results for Spectral Terms of a Riemannian Foliation (V Slesar); On the Group of Foliation Preserving Diffeomorphisms (T Tsuboi); and other papers. Readership: Researchers and graduate students in such areas of mathematics as foliations, dynamical systems (Anosov and Morse-Smale, in particular), Riemannian and conformal
geometry; and in other fields such as mathematical physics, non-commutative geometry and analysis on manifolds.
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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