TY  - BOOK
AU  - Gallier,Jean H.
AU  - Xu,Dianna
TI  - Guide to the Classification Theorem for Compact Surfaces 
T2  - Geometry and computing,
SN  - 9783642343636 (alk. paper)
AV  - QA326 .G35 2013
U1  - 516.352 G136G 23
PY  - 2013///
CY  - Heidelberg
PB  - Springer-Verlag
KW  - Topological algebras
KW  - Classification Theorem
KW  - Compact Surfces
KW  - Mathematics
N1  - Includes bibliographical references and indexes; 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; the cross-cap and the Steiner roman surface -- Proof of proposition 5.1 -- Topological preliminaries -- History of the classification theorem -- Every surface can be triangulated
N2  - 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-centered 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.--
ER  -