Foundations of Differentiable Manifolds and Lie Groups

Author: Frank W. Warner

Publisher: Springer Science & Business Media

ISBN: 1475717997

Category: Mathematics

Page: 276

View: 9020

Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem.
Posted in Mathematics

Compact Lie Groups

Author: Mark R. Sepanski

Publisher: Springer Science & Business Media

ISBN: 0387491589

Category: Mathematics

Page: 201

View: 4922

Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Coverage includes the construction of the Spin groups, Schur Orthogonality, the Peter-Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel-Weil Theorem. The book develops the necessary Lie algebra theory with a streamlined approach focusing on linear Lie groups.
Posted in Mathematics

Stein Manifolds and Holomorphic Mappings

The Homotopy Principle in Complex Analysis

Author: Franc Forstnerič

Publisher: Springer

ISBN: 3319610589

Category: Mathematics

Page: 562

View: 8289

This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds. Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory. Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka theory and the theory of holomorphic automorphisms of complex Euclidean spaces and of other complex manifolds with large automorphism groups./div
Posted in Mathematics

Séminaire de Probabilités XLII

Author: Catherine Donati-Martin,Michel Émery,Alain Rouault,Christophe Stricker

Publisher: Springer

ISBN: 3642017630

Category: Mathematics

Page: 449

View: 2279

This book offers an introduction to rough paths. Coverage also includes the interface between analysis and probability to special processes, Lévy processes and Lévy systems, representation of Gaussian processes, filtrations and quantum probability.
Posted in Mathematics

Publicationes Mathematicae

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 8855

Posted in Mathematics

Bericht

Report

Author: Jyväskylän yliopisto. Matematiikan laitos,Osmo Pekonen

Publisher: N.A

ISBN: 9789516799608

Category: Mathematics

Page: 46

View: 9957

Posted in Mathematics

Metric Structures in Differential Geometry

Author: Gerard Walschap

Publisher: Springer Science & Business Media

ISBN: 9780387204307

Category: Mathematics

Page: 229

View: 9387

This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres.
Posted in Mathematics

Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 2017

Posted in American literature

Proceedings of the Japan Academy

mathematical sciences

Author: Nihon Gakushiin

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 8931

Posted in Mathematics

Symplectic torus actions

Author: Alvaro Pelayo

Publisher: N.A

ISBN: N.A

Category:

Page: N.A

View: 5725

Posted in

Introduction to Differentiable Manifolds

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 0387954775

Category: Mathematics

Page: 250

View: 2791

This book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. The author's book, Fundamentals of Differential Geometry, can be viewed as a continuation of the present book. Since this book is intended as a text to follow advanced calculus, manifolds are assumed finite dimensional. The author has made numerous corrections to this new edition, and he has also added a chapter on applications of Stokes' Theorem.
Posted in Mathematics

Maß und Kategorie

Author: J.C. Oxtoby

Publisher: Springer-Verlag

ISBN: 364296074X

Category: Mathematics

Page: 112

View: 7942

Dieses Buch behandelt hauptsächlich zwei Themenkreise: Der Bairesche Kategorie-Satz als Hilfsmittel für Existenzbeweise sowie Die "Dualität" zwischen Maß und Kategorie. Die Kategorie-Methode wird durch viele typische Anwendungen erläutert; die Analogie, die zwischen Maß und Kategorie besteht, wird nach den verschiedensten Richtungen hin genauer untersucht. Hierzu findet der Leser eine kurze Einführung in die Grundlagen der metrischen Topologie; außerdem werden grundlegende Eigenschaften des Lebesgue schen Maßes hergeleitet. Es zeigt sich, daß die Lebesguesche Integrationstheorie für unsere Zwecke nicht erforderlich ist, sondern daß das Riemannsche Integral ausreicht. Weiter werden einige Begriffe aus der allgemeinen Maßtheorie und Topologie eingeführt; dies geschieht jedoch nicht nur der größeren Allgemeinheit wegen. Es erübrigt sich fast zu erwähnen, daß sich die Bezeichnung "Kategorie" stets auf "Bairesche Kategorie" be zieht; sie hat nichts zu tun mit dem in der homologischen Algebra verwendeten Begriff der Kategorie. Beim Leser werden lediglich grundlegende Kenntnisse aus der Analysis und eine gewisse Vertrautheit mit der Mengenlehre vorausgesetzt. Für die hier untersuchten Probleme bietet sich in natürlicher Weise die mengentheoretische Formulierung an. Das vorlie gende Buch ist als Einführung in dieses Gebiet der Analysis gedacht. Man könnte es als Ergänzung zur üblichen Grundvorlesung über reelle Analysis, als Grundlage für ein Se minar oder auch zum selbständigen Studium verwenden. Bei diesem Buch handelt es sich vorwiegend um eine zusammenfassende Darstellung; jedoch finden sich in ihm auch einige Verfeinerungen bekannter Resultate, namentlich Satz 15.6 und Aussage 20.4. Das Literaturverzeichnis erhebt keinen Anspruch auf Vollständigkeit. Häufig werden Werke zitiert, die weitere Literaturangaben enthalten.
Posted in Mathematics

Geometry & Topology

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Geometry

Page: N.A

View: 9989

Fully refereed international journal dealing with all aspects of geometry and topology and their applications.
Posted in Geometry

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2979

Posted in Mathematics

German books in print

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Austria

Page: N.A

View: 6651

Posted in Austria