A Topology Primer
by Klaus Wirthmüller
Publisher: Technische Universität Kaiserslautern 2002
Number of pages: 197
The purpose of this text is to make familiar with the basics of topology, to give a concise introduction to homotopy, and to make students familiar with homology. Readers are expected to have successfully completed their first year courses in analysis and linear algebra.
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by Jean Gallier, Dianna Xu
In this book the authors 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.
by Peter Petersen - UCLA
These notes are a supplement to a first year graduate course in manifold theory. These are the topics covered: Manifolds (Smooth Manifolds, Projective Space, Matrix Spaces); Basic Tensor Analysis; Basic Cohomology Theory; Characteristic Classes.
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Contents: Important examples of topological spaces; Constructions; Homotopy and homotopy equivalence; CW-complexes and homotopy; Fundamental group; Covering spaces; Higher homotopy groups; Fiber bundles; Suspension Theorem and Whitehead product; etc.
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A thorough treatment of homology operations and of their application to the calculation of the homologies of various spaces. The book studies an up to homotopy notion of an algebra over a monad and its role in the theory of iterated loop spaces.