A Guide to the Classification Theorem for Compact Surfaces / by Jean Gallier, Dianna Xu.

Format:

Book

Author/Creator:

Gallier, Jean, author.

Xu, Dianna, author.

Contributor:

SpringerLink (Online service)

Series:

Geometry and computing 1866-6795

Geometry and Computing, 1866-6795

Language:

English

Subjects (All):

Topology.

Manifolds (Mathematics).

Complex manifolds.

Algebraic topology.

Manifolds and Cell Complexes (incl. Diff.Topology).

Algebraic Topology.

Local Subjects:

Topology.

Manifolds and Cell Complexes (incl. Diff.Topology).

Algebraic Topology.

Physical Description:

1 online resource (XII, 178 pages 78 illustrations, 20 illustrations in color.)

Edition:

First edition 2013.

Contained In:

Springer Nature eBook

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.

System Details:

text file PDF

Summary:

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.

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 .

Other Format:

Printed edition:

ISBN:

9783642343643

Access Restriction:

Restricted for use by site license.