The Classification Theorem for Compact Surfaces
by Jean Gallier, Dianna Xu
Number of pages: 134
The topic of this book is the classification theorem for compact surfaces. We present the technical tools needed for proving rigorously the classification theorem, give a detailed proof using these tools, and also discuss the history of the theorem and its various "proofs".
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by J. P. May - University Of Chicago Press
This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics. Most chapters end with problems that further explore and refine the concepts presented.
by G. de Rham - Tata Institute of Fundamental Research
These notes were intended as a first introduction to algebraic Topology. Contents: Definition and general properties of the fundamental group; Free products of groups and their quotients; On calculation of fundamental groups; and more.
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This is an introduction to simplicial sets and simplicial homotopy theory with a focus on the combinatorial aspects of the theory and their geometric/topological origins. Accessible to students familiar with the fundamentals of algebraic topology.