A Guide to the Classification Theorem for Compact Surfaces (Geometry and Computing, 9, Band 9) - Hardcover

Buch 8 von 12: Geometry and Computing

Gallier, Jean; Xu, Dianna

 
9783642343636: A Guide to the Classification Theorem for Compact Surfaces (Geometry and Computing, 9, Band 9)
Hardcover
ISBN 10: 3642343635 ISBN 13: 9783642343636
Verlag: Springer, 2013

Inhaltsangabe

This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example.

Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology.

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This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example.

Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology.

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Verlag
Springer
Erscheinungsdatum
2013
Sprache
Englisch
ISBN 10 
3642343635
ISBN 13 
9783642343636
Einband
Gebundene Ausgabe
Anzahl der Seiten
190
Kontakt zum Hersteller
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Weitere beliebte Ausgaben desselben Titels

9783642437106: A Guide to the Classification Theorem for Compact Surfaces (Geometry and Computing, Band 9)

Vorgestellte Ausgabe

ISBN 10:  3642437109 ISBN 13:  9783642437106
Verlag: Springer, 2015
Softcover