Introduction to Topological Manifolds: 202 (Graduate Texts in Mathematics) - Hardcover

Lee, John

Hardcover

ISBN 10: 1441979395 ISBN 13: 9781441979391

Verlag: Springer, 2010

Inhaltsangabe

<P>THIS BOOK IS AN INTRODUCTION TO MANIFOLDS AT THE BEGINNING GRADUATE LEVEL, AND ACCESSIBLE TO ANY STUDENT WHO HAS COMPLETED A SOLID UNDERGRADUATE DEGREE IN MATHEMATICS. IT CONTAINS THE ESSENTIAL TOPOLOGICAL IDEAS THAT ARE NEEDED FOR THE FURTHER STUDY OF MANIFOLDS, PARTICULARLY IN THE CONTEXT OF DIFFERENTIAL GEOMETRY, ALGEBRAIC TOPOLOGY, AND RELATED FIELDS.</P><P>ALTHOUGH THIS SECOND EDITION HAS THE SAME BASIC STRUCTURE AS THE FIRST EDITION, IT HAS BEEN EXTENSIVELY REVISED AND CLARIFIED; NOT A SINGLE PAGE HAS BEEN LEFT UNTOUCHED.  THE MAJOR CHANGES INCLUDE A NEW INTRODUCTION TO CW COMPLEXES (REPLACING MOST OF THE MATERIAL ON SIMPLICIAL COMPLEXES IN CHAPTER 5); EXPANDED TREATMENTS OF MANIFOLDS WITH BOUNDARY, LOCAL COMPACTNESS, GROUP ACTIONS, AND PROPER MAPS; AND A NEW SECTION ON PARACOMPACTNESS.</P>

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From the reviews of the second edition:

“An excellent introduction to both point-set and algebraic topology at the early-graduate level, using manifolds as a primary source of examples and motivation. ... The author has ... fulfilled his objective of integrating a study of manifolds into an introductory course in general and algebraic topology. This text is well-organized and clearly written, with a good blend of motivational discussion and mathematical rigor. ... Any student who has gone through this book should be well-prepared to pursue the study of differential geometry ... .” (Mark Hunacek, The Mathematical Association of America, March, 2011)

“This book is designed for first year graduate students as an introduction to the topology of manifolds. ... The book can be read with advantage by any graduate student with a good undergraduate background, and indeed by many upper class undergraduates. It can be used for self study or as a text book for a fine geometrically flavored introduction to manifolds. One which provides excellent motivation for studying the machinery needed for more advanced work.” (Jonathan Hodgson, Zentralblatt MATH, Vol. 1209, 2011)

Reseña del editor:

This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields.

Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched.  The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.

Über diese Auflage

• Verlag: Springer
• Erscheinungsdatum: 2010
• ISBN 10: 1441979395
• ISBN 13: 9781441979391
• Einband: Tapa dura
• Auflage: 2
• Anzahl der Seiten: 452