Introduction to Differential and Algebraic Topology

Yu. G. Borisovich

ISBN 10: 9048145589 / ISBN 13: 9789048145584

Editore: Springer Netherlands, Springer Netherlands, 2010

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Druck auf Anfrage Neuware - Printed after ordering - Topology as a subject, in our opinion, plays a central role in university education. It is not really possible to design courses in differential geometry, mathematical analysis, differential equations, mechanics, functional analysis that correspond to the temporary state of these disciplines without involving topological concepts. Therefore, it is essential to acquaint students with topo logical research methods already in the first university courses. This textbook is one possible version of an introductory course in topo logy and elements of differential geometry, and it absolutely reflects both the authors' personal preferences and experience as lecturers and researchers. It deals with those areas of topology and geometry that are most closely related to fundamental courses in general mathematics. The educational material leaves a lecturer a free choice in designing his own course or his own seminar. We draw attention to a number of particularities in our book. The first chap ter, according to the authors' intention, should acquaint readers with topolo gical problems and concepts which arise from problems in geometry, analysis, and physics. Here, general topology (Ch. 2) is presented by introducing con structions, for example, related to the concept of quotient spaces, much earlier than various other notions of general topology thus making it possible for students to study important examples of manifolds (two-dimensional surfaces, projective spaces, orbit spaces, etc.) as topological spaces, immediately.

Codice articolo 9789048145584

Dati bibliografici

• Titolo: Introduction to Differential and Algebraic Topology
• Editore: Springer Netherlands, Springer Netherlands
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 9048145589
• ISBN 13: 9789048145584
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 28 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 28 millimetri di profondità
• Peso: 762 grammi

Descrizione articolo

Riassunto

Topology as a subject, in our opinion, plays a central role in university education. It is not really possible to design courses in differential geometry, mathematical analysis, differential equations, mechanics, functional analysis that correspond to the temporary state of these disciplines without involving topological concepts. Therefore, it is essential to acquaint students with topo­ logical research methods already in the first university courses. This textbook is one possible version of an introductory course in topo­ logy and elements of differential geometry, and it absolutely reflects both the authors' personal preferences and experience as lecturers and researchers. It deals with those areas of topology and geometry that are most closely related to fundamental courses in general mathematics. The educational material leaves a lecturer a free choice in designing his own course or his own seminar. We draw attention to a number of particularities in our book. The first chap­ ter, according to the authors' intention, should acquaint readers with topolo­ gical problems and concepts which arise from problems in geometry, analysis, and physics. Here, general topology (Ch. 2) is presented by introducing con­ structions, for example, related to the concept of quotient spaces, much earlier than various other notions of general topology thus making it possible for students to study important examples of manifolds (two-dimensional surfaces, projective spaces, orbit spaces, etc.) as topological spaces, immediately.

Contenuti

Preface. 1: First Notions of Topology. 2: General Topology. 3: Homotopy Theory. 4: Manifolds and Fiberings. 5: Homology Theory. References. Subject Index. About the authors and the book.