Mod Two Homology and Cohomology

Nonfiction, Science & Nature, Mathematics, Topology, Geometry
Cover of the book Mod Two Homology and Cohomology by Jean-Claude Hausmann, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Jean-Claude Hausmann ISBN: 9783319093543
Publisher: Springer International Publishing Publication: January 8, 2015
Imprint: Springer Language: English
Author: Jean-Claude Hausmann
ISBN: 9783319093543
Publisher: Springer International Publishing
Publication: January 8, 2015
Imprint: Springer
Language: English

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, Poincaré 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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, Poincaré 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.

More books from Springer International Publishing

Cover of the book Cloud Computing and Services Science by Jean-Claude Hausmann
Cover of the book The Struggles of Identity, Education, and Agency in the Lives of Undocumented Students by Jean-Claude Hausmann
Cover of the book Computational Science/Intelligence and Applied Informatics by Jean-Claude Hausmann
Cover of the book The Global Crisis of 2008 and Keynes's General Theory by Jean-Claude Hausmann
Cover of the book The Soils of Ireland by Jean-Claude Hausmann
Cover of the book The Velestino Hoard by Jean-Claude Hausmann
Cover of the book Activity Monitoring by Multiple Distributed Sensing by Jean-Claude Hausmann
Cover of the book The Invention of Time and Space by Jean-Claude Hausmann
Cover of the book Accelerated Cosmic Expansion by Jean-Claude Hausmann
Cover of the book Human Rights and Relative Universalism by Jean-Claude Hausmann
Cover of the book The Bleak Political Implications of Socratic Religion by Jean-Claude Hausmann
Cover of the book Perspectives on Interrogative Models of Inquiry by Jean-Claude Hausmann
Cover of the book Advances in Computational Intelligence by Jean-Claude Hausmann
Cover of the book Step Wise Protocols for Somatic Embryogenesis of Important Woody Plants by Jean-Claude Hausmann
Cover of the book Alternative Energy Sources and Technologies by Jean-Claude Hausmann
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy