Cohomology and homology modulo 2 helps the reader grasp more readily the basics of a major tool in algebraic topology. Compared to a more general approach to (co)homology this refreshing approach has many pedagogical advantages: 1. It leads more quickly to the essentials of the subject, 2. An absence of signs and orientation considerations simplifies the theory, 3. Computations and advanced applications can be presented at an earlier stage, 4. Simple geometrical interpretations of (co)chains. Mod 2 (co)homology was developed in the first quarter of the twentieth century as an alternative to integral homology, before both became particular cases of (co)homology with arbitrary coefficients. The first chapters of this book may serve as a basis for a graduatelevel introductory course to (co)homology. Simplicial and singular mod 2 (co)homology are introduced, with their products and Steenrod squares, as well as equivariant cohomology. Classical applications include Brouwer's fixed point theorem, Poincare duality, BorsukUlam theorem, Hopf invariant, Smith theory, Kervaire invariant, etc. The cohomology of flag manifolds is treated in detail (without spectral sequences), including the relationship between StiefelWhitney classes and Schubert calculus. More recent developments are also covered, including topological complexity, face spaces, equivariant Morse theory, conjugation spaces, polygon spaces, amongst others. Each chapter ends with exercises, with some hints and answers at the end of the book.
About JeanClaude Hausmann
JeanClaude Hausmann is honorary professor of Mathematics at the University of Geneva. His domains of interest include topology of highdimensional manifolds, with applications to configuration spaces inspired by topological robotics and Hamiltonian geometry.Details Book
Author  :  JeanClaude Hausmann 
Publisher  :  Springer International Publishing AG 
Data Published  :  20 January 2015 
ISBN  :  3319093533 
EAN  :  9783319093536 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  535 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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