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

By Jean Gallier,Dianna Xu

This welcome boon for college kids of algebraic topology cuts a much-needed vital direction among different texts whose remedy of the type theorem for compact surfaces is both too formalized and complicated for these with out distinctive historical past wisdom, or too casual to come up with the money for scholars a finished perception into the topic. Its committed, student-centred technique info a near-complete evidence of this theorem, broadly widespread for its efficacy and formal good looks. The authors current the technical instruments had to installation the strategy successfully in addition to demonstrating their use in a basically dependent, labored example.

Ideal for college students whose mastery of algebraic topology could be a work-in-progress, the textual content introduces key notions corresponding to primary teams, homology teams, and the Euler-Poincaré attribute. those must haves are the topic of specified appendices that permit concentrated, discrete studying the place it really is required, with no interrupting the rigorously deliberate constitution of the center exposition. lightly guiding readers in the course of the rules, thought, and purposes of the class theorem, the authors objective to foster actual self assurance in its use and in so doing motivate readers to maneuver directly to a deeper exploration of the flexible and helpful suggestions to be had in algebraic topology.

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