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Geometry and Computing #9: A Guide to the Classification Theorem for Compact Surfaces

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Geometry and Computing #9: A Guide to the Classification Theorem for Compact Surfaces Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This book offers a detailed proof of the classification theorem for compact surfaces. It presents the technical tools needed to deploy the method effectively as well as demonstrates their use in a clearly structured, worked example.

Table of Contents

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​.

Product Details

ISBN:
9783642343636
Author:
Gallier, Jean
Publisher:
Springer
Author:
Xu, Dianna
Subject:
Topology
Subject:
Algebraic topology
Subject:
Cell complex
Subject:
Compact Surfaces
Subject:
Triangulation.
Subject:
Manifolds and Cell Complexes (incl. Diff.Topology)
Subject:
MATHEMATICS / Topology
Copyright:
Edition Description:
2013
Series:
Geometry and Computing
Series Volume:
9
Publication Date:
20130131
Binding:
HARDCOVER
Language:
English
Pages:
190
Dimensions:
235 x 155 mm

Related Subjects


Science and Mathematics » Materials Science » Textiles
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Topology

Geometry and Computing #9: A Guide to the Classification Theorem for Compact Surfaces New Hardcover
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Product details 190 pages Springer - English 9783642343636 Reviews:
"Synopsis" by , This book offers a detailed proof of the classification theorem for compact surfaces. It presents the technical tools needed to deploy the method effectively as well as demonstrates their use in a clearly structured, worked example.
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