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＜電子ブック＞
A Guide to the Classification Theorem for Compact Surfaces / by Jean Gallier, Dianna Xu
(Geometry and Computing. ISSN:18666809)

版	1st ed. 2013.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2013
本文言語	英語
大きさ	XII, 178 p. 78 illus., 20 illus. in color : online resource
著者標目	*Gallier, Jean author Xu, Dianna author SpringerLink (Online service)
件　名	LCSH:Topology LCSH:Manifolds (Mathematics) LCSH:Algebraic topology FREE:Topology FREE:Manifolds and Cell Complexes FREE:Algebraic Topology
一般注記	The Classification Theorem: Informal Presentation -- Surfaces -- Simplices, Complexes, and Triangulations -- The Fundamental Group, Orientability -- Homology Groups -- The Classification Theorem for Compact Surfaces -- Viewing the Real Projective Plane in R3 -- Proof of Proposition 5.1 -- Topological Preliminaries -- History of the Classification Theorem -- Every Surface Can be Triangulated -- Notes 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 HTTP:URL=https://doi.org/10.1007/978-3-642-34364-3

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