Mod Two Homology and Cohomology (Paperback, 2014 ed.)

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 graduate-level 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, Borsuk-Ulam theorem, Hopf invariant, Smith theory, Kervaire invariant, etc. The cohomology of flag manifolds is treated in detail (without spectral sequences), including the relationship between Stiefel-Whitney 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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Universitext
Release date:	2015
First published:	2014
Authors:	Jean-Claude Hausmann
Dimensions:	235 x 155 x 25mm (L x W x T)
Format:	Paperback
Pages:	535
Edition:	2014 ed.
ISBN-13:	978-3-319-09353-6
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Analytic geometry Books > Science & Mathematics > Mathematics > Topology > Algebraic topology
LSN:	3-319-09353-3
Barcode:	9783319093536

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