Topics in topology: The signature theorem and some of its applications
by Liviu I. Nicolaescu
Publisher: University of Notre Dame 2008
Number of pages: 159
The author discusses several exciting topological developments that took place during the fifties decade which radically changed the way we think about many issues. Topics covered: Poincare duality, Thom isomorphism, Euler, Chern and Pontryagin classes, cobordisms groups, signature formula.
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by Klaus Wirthmüller - Technische Universität Kaiserslautern
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 knowledge of analysis and linear algebra.
by Peter Saveliev - Intelligent Perception
The text follows the content of a fairly typical, two-semester, first course in topology. Some of the topics are: the shape of the universe, configuration spaces, digital image analysis, data analysis, social choice, and, of course, calculus.
by Boris Botvinnik - University of Oregon
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.
by Andrew Ranicki, Norman Levitt, Frank Quinn - Springer
The book present original research on a wide range of topics in modern topology: the algebraic K-theory of spaces, the algebraic obstructions to surgery and finiteness, geometric and chain complexes, characteristic classes, and transformation groups.