Overview

Dieses Lehrbuch bietet eine Einführung in die Differentialgeometrie auf Faserbündeln. Nach einem Kapitel über Lie-Gruppen und homogene Räume werden lokal-triviale Faserungen, insbesondere die Hauptfaserbündel und zu ihnen assoziierte Vektorbündel, besprochen. Es folgen die grundlegenden Begriffe der Differentialrechnung auf Faserbündeln: Zusammenhang, Krümmung, Parallelverschiebung und kovariante Ableitung. Anschließend werden die Holonomiegruppen vorgestellt, die zentrale Bedeutung in der Differentialgeometrie haben. Als Anwendungen werden charakteristische Klassen und die Yang-Mills-Gleichung behandelt. Zahlreiche Aufgaben mit Lösungshinweisen helfen, das Gelernte zu vertiefen. Das Buch richtet sich vor allem an Studenten der Mathematik und Physik im Masterstudium. Es stellt mathematische Grundlagen bereit, die in Vorlesungen zur Eichfeldtheorie in der theoretischen und mathematischen Physik Anwendung finden.

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9783642385384

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Reviews

From the book reviews: This textbook provides in an attractive and rigorous manner, an introduction to the differential geometry of fiber bundles. The book targets as main audience the students whose subjects of study are mathematics and physics. All in all, it represents an excellent primary source for learning the mathematical foundations of gauge field theory. (Vladimir Balan, zbMATH, Vol. 1297, 2014)

From the reviews: The aim of the book is to introduce students with background in Riemannian geometry to the theory of connections on principal bundles and holonomy. The exposition of the material is clear and very detailed. Many examples and figures illustrate the concepts and theorems. At the end of each chapter there are exercises. Most of them provide further interesting examples. Solutions are given at the end of the book. This book is definitely a welcome addition to the German textbook market. (Thomas Puttmann, Zentralblatt MATH, Vol. 1175, 2010) This textbook provides a thorough introduction into the theory of connections on principal fiber bundles and holonomy. Each chapter of this carefully prepared text is closed by a number of well-selected exercises. Their solutions are given at the end of the book together with an appendix collecting the necessary prerequisites from Riemannian geometry. (R. Steinbauer, Monatshefte fur Mathematik, Vol. 165 (3-4), March, 2012) From the book reviews: This textbook provides in an attractive and rigorous manner, an introduction to the differential geometry of fiber bundles. The book targets as main audience the students whose subjects of study are mathematics and physics. All in all, it represents an excellent primary source for learning the mathematical foundations of gauge field theory. (Vladimir Balan, zbMATH, Vol. 1297, 2014) From the book reviews: This textbook provides in an attractive and rigorous manner, an introduction to the differential geometry of fiber bundles. The book targets as main audience the students whose subjects of study are mathematics and physics. All in all, it represents an excellent primary source for learning the mathematical foundations of gauge field theory. (Vladimir Balan, zbMATH, Vol. 1297, 2014) From the reviews: The aim of the book is to introduce students with background in Riemannian geometry to the theory of connections on principal bundles and holonomy. The exposition of the material is clear and very detailed. Many examples and figures illustrate the concepts and theorems. At the end of each chapter there are exercises. Most of them provide further interesting examples. Solutions are given at the end of the book. This book is definitely a welcome addition to the German textbook market. (Thomas Puttmann, Zentralblatt MATH, Vol. 1175, 2010) This textbook provides a thorough introduction into the theory of connections on principal fiber bundles and holonomy. Each chapter of this carefully prepared text is closed by a number of well-selected exercises. Their solutions are given at the end of the book together with an appendix collecting the necessary prerequisites from Riemannian geometry. (R. Steinbauer, Monatshefte fur Mathematik, Vol. 165 (3-4), March, 2012) From the reviews: The aim of the book is to introduce students with background in Riemannian geometry to the theory of connections on principal bundles and holonomy. The exposition of the material is clear and very detailed. Many examples and figures illustrate the concepts and theorems. At the end of each chapter there are exercises. Most of them provide further interesting examples. Solutions are given at the end of the book. This book is definitely a welcome addition to the German textbook market. (Thomas P ttmann, Zentralblatt MATH, Vol. 1175, 2010)

From the reviews: The aim of the book is to introduce students with background in Riemannian geometry to the theory of connections on principal bundles and holonomy. The exposition of the material is clear and very detailed. Many examples and figures illustrate the concepts and theorems. At the end of each chapter there are exercises. Most of them provide further interesting examples. Solutions are given at the end of the book. This book is definitely a welcome addition to the German textbook market. (Thomas Puttmann, Zentralblatt MATH, Vol. 1175, 2010) This textbook provides a thorough introduction into the theory of connections on principal fiber bundles and holonomy. Each chapter of this carefully prepared text is closed by a number of well-selected exercises. Their solutions are given at the end of the book together with an appendix collecting the necessary prerequisites from Riemannian geometry. (R. Steinbauer, Monatshefte fur Mathematik, Vol. 165 (3-4), March, 2012)

From the reviews: The aim of the book is to introduce students with background in Riemannian geometry to the theory of connections on principal bundles and holonomy. The exposition of the material is clear and very detailed. Many examples and figures illustrate the concepts and theorems. At the end of each chapter there are exercises. Most of them provide further interesting examples. Solutions are given at the end of the book. This book is definitely a welcome addition to the German textbook market. (Thomas Puttmann, Zentralblatt MATH, Vol. 1175, 2010) This textbook provides a thorough introduction into the theory of connections on principal fiber bundles and holonomy. Each chapter of this carefully prepared text is closed by a number of well-selected exercises. Their solutions are given at the end of the book together with an appendix collecting the necessary prerequisites from Riemannian geometry. (R. Steinbauer, Monatshefte fur Mathematik, Vol. 165 (3-4), March, 2012) From the book reviews: This textbook provides in an attractive and rigorous manner, an introduction to the differential geometry of fiber bundles. ... The book targets as main audience the students whose subjects of study are mathematics and physics. All in all, it represents an excellent primary source for learning the mathematical foundations of gauge field theory. (Vladimir Balan, zbMATH, Vol. 1297, 2014) From the book reviews: This textbook provides in an attractive and rigorous manner, an introduction to the differential geometry of fiber bundles. The book targets as main audience the students whose subjects of study are mathematics and physics. All in all, it represents an excellent primary source for learning the mathematical foundations of gauge field theory. (Vladimir Balan, zbMATH, Vol. 1297, 2014) From the book reviews: This textbook provides in an attractive and rigorous manner, an introduction to the differential geometry of fiber bundles. The book targets as main audience the students whose subjects of study are mathematics and physics. All in all, it represents an excellent primary source for learning the mathematical foundations of gauge field theory. (Vladimir Balan, zbMATH, Vol. 1297, 2014) From the reviews: The aim of the book is to introduce students with background in Riemannian geometry to the theory of connections on principal bundles and holonomy. The exposition of the material is clear and very detailed. Many examples and figures illustrate the concepts and theorems. At the end of each chapter there are exercises. Most of them provide further interesting examples. Solutions are given at the end of the book. This book is definitely a welcome addition to the German textbook market. (Thomas Puttmann, Zentralblatt MATH, Vol. 1175, 2010) This textbook provides a thorough introduction into the theory of connections on principal fiber bundles and holonomy. Each chapter of this carefully prepared text is closed by a number of well-selected exercises. Their solutions are given at the end of the book together with an appendix collecting the necessary prerequisites from Riemannian geometry. (R. Steinbauer, Monatshefte fur Mathematik, Vol. 165 (3-4), March, 2012) From the reviews: The aim of the book is to introduce students with background in Riemannian geometry to the theory of connections on principal bundles and holonomy. The exposition of the material is clear and very detailed. Many examples and figures illustrate the concepts and theorems. At the end of each chapter there are exercises. Most of them provide further interesting examples. Solutions are given at the end of the book. This book is definitely a welcome addition to the German textbook market. (Thomas P ttmann, Zentralblatt MATH, Vol. 1175, 2010)

Author Information

Prof. Dr. Helga Baum, Humboldt-Universität Berlin, Institut für Mathematik

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