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 Cognitive, Conative and Behavioral Neurology by Jean-Claude Hausmann
Cover of the book Electrochemical Science for a Sustainable Society by Jean-Claude Hausmann
Cover of the book Myelodysplastic Syndromes by Jean-Claude Hausmann
Cover of the book Analysis and Partial Differential Equations: Perspectives from Developing Countries by Jean-Claude Hausmann
Cover of the book Knocking in Gasoline Engines by Jean-Claude Hausmann
Cover of the book Confronting Gun Violence in America by Jean-Claude Hausmann
Cover of the book Earthquake Geotechnical Engineering Design by Jean-Claude Hausmann
Cover of the book Introducing the Oscillations Based Paradigm by Jean-Claude Hausmann
Cover of the book The Protection of Traditional Cultural Expressions in Africa by Jean-Claude Hausmann
Cover of the book Cormac McCarthy’s Philosophy by Jean-Claude Hausmann
Cover of the book Teaching Graphic Novels in the English Classroom by Jean-Claude Hausmann
Cover of the book Adrenal Disorders by Jean-Claude Hausmann
Cover of the book The Incomputable by Jean-Claude Hausmann
Cover of the book Pelton Turbines by Jean-Claude Hausmann
Cover of the book Self- and Co-regulation in Cybercrime, Cybersecurity and National Security 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