by Peter Petersen
Publisher: UCLA 2010
Number of pages: 77
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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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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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.
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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.