A guide to the classification theorem for compact surfaces [Documento electrónico] / Jean Gallier, Dianna Xu
Language: eng.Country: Germany.Publication: Berlin, Heidelberg : Springer Berlin Heidelberg, 2013Description: XII, 178 p. ISBN: 978-3-642-34364-3.Series: Geometry and ComputingSubject - Topical Name: 6383Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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E-Books | Biblioteca NOVA FCT Online | Não Ficção | QA611.SPR FCT 82614 (Browse shelf(Opens below)) | 1 | Available |
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QA611.SPR FCT 82296 Topologia | QA611.SPR FCT 82342 Classi caratteristiche e questioni connesse | QA611.SPR FCT 82444 Topological methods in data analysis and visualization | QA611.SPR FCT 82614 A guide to the classification theorem for compact surfaces | QA611.SPR FCT 82819 Geometric aspects of general topology | QA611.SPR FCT 82922 Topologia | QA611.SPR FCT 82964 Recent progress in general topology III |
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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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