A Guide to the Classification Theorem for Compact Surfaces

  • Jean Gallier
  • Dianna Xu

Part of the Geometry and Computing book series (GC, volume 9)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Jean Gallier, Dianna Xu
    Pages 1-20
  3. Jean Gallier, Dianna Xu
    Pages 21-25
  4. Jean Gallier, Dianna Xu
    Pages 27-35
  5. Jean Gallier, Dianna Xu
    Pages 37-51
  6. Jean Gallier, Dianna Xu
    Pages 53-77
  7. Jean Gallier, Dianna Xu
    Pages 79-103
  8. Back Matter
    Pages 105-178

About this book


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.


Algebraic Topology Cell complex Compact Surfaces Triangulation

Authors and affiliations

  • Jean Gallier
    • 1
  • Dianna Xu
    • 2
  1. 1., Dept of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2., Dept. of Computer ScienceBryn Mawr CollegeBryn MawrUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-34363-6
  • Online ISBN 978-3-642-34364-3
  • Series Print ISSN 1866-6795
  • Series Online ISSN 1866-6809
  • Buy this book on publisher's site