A Guide to the Classification Theorem for Compact Surfaces (Paperback, 2013 ed.)

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-Poincare 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.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Geometry and Computing, 9
Release date:	March 2015
First published:	2013
Authors:	Jean Gallier • Dianna Xu
Dimensions:	235 x 155 x 10mm (L x W x T)
Format:	Paperback
Pages:	178
Edition:	2013 ed.
ISBN-13:	978-3-642-43710-6
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Analytic geometry Books > Science & Mathematics > Mathematics > Topology > Algebraic topology Promotions
LSN:	3-642-43710-9
Barcode:	9783642437106

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