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Foliations: Dynamics, Geometry and Topology

Masayuki Asaoka, Aziz El Kacimi Alaoui, Steven Hurder, Ken Richardson (Autoren)

Jesús Álvarez López, Marcel Nicolau (Herausgeber)

Buch | Softcover

IX, 198 Seiten

2014 | 2014
Springer Basel (Verlag)
978-3-0348-0870-5 (ISBN)

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This book is an introduction to several active research topics in Foliation Theory and its connections with other areas. It contains expository lectures showing the diversity of ideas and methods converging in the study of foliations. The lectures by Aziz El Kacimi Alaoui provide an introduction to Foliation Theory with emphasis on examples and transverse structures. Steven Hurder's lectures apply ideas from smooth dynamical systems to develop useful concepts in the study of foliations: limit sets and cycles for leaves, leafwise geodesic flow, transverse exponents, Pesin Theory and hyperbolic, parabolic and elliptic types of foliations. The lectures by Masayuki Asaoka compute the leafwise cohomology of foliations given by actions of Lie groups, and apply it to describe deformation of those actions. In his lectures, Ken Richardson studies the properties of transverse Dirac operators for Riemannian foliations and compact Lie group actions, and explains a recently proved index formula. Besides students and researchers of Foliation Theory, this book will be interesting for mathematicians interested in the applications to foliations of subjects like Topology of Manifolds, Differential Geometry, Dynamics, Cohomology or Global Analysis.

Fundamentals of Foliation Theory.- Foliation Dynamics.- Deformation of Locally Free Actions and Leafwise Cohomology.- Transversal Dirac Operators on Distributions, Foliations, and G-Manifolds.

"This book contains the lecture notes of four courses on several topics with rather different flavor, which are linked by their relation with Foliation Theory. ... the courses will be very helpful for any reader that wants to get quickly introduced to any of these lines of research." (Jesus A. Álvarez López, zbMATH 1318.57001, 2015)

Erscheint lt. Verlag	22.12.2014
Reihe/Serie	Advanced Courses in Mathematics - CRM Barcelona
Zusatzinfo	IX, 198 p. 20 illus., 10 illus. in color.
Verlagsort	Basel
Sprache	englisch
Maße	168 x 240 mm
Gewicht	422 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	leafwise cohomology • leafwise geodesic flow • limit set • locally free action • transverse Dirac operator • transverse structure
ISBN-10	3-0348-0870-4 / 3034808704
ISBN-13	978-3-0348-0870-5 / 9783034808705
Zustand	Neuware