Mod Two Homology and Cohomology (Universitext) by Jean-Claude Hausmann

By Jean-Claude Hausmann

Cohomology and homology modulo 2 is helping the reader clutch extra without problems the fundamentals of a huge instrument in algebraic topology. in comparison to a extra normal method of (co)homology this clean strategy has many pedagogical advantages:

1. It leads extra fast to the necessities of the subject,
2. a scarcity of symptoms and orientation concerns simplifies the theory,
3. Computations and complicated functions will be provided at an prior level,
4. uncomplicated geometrical interpretations of (co)chains.

Mod 2 (co)homology was once constructed within the first sector of the 20 th century as a substitute to crucial homology, earlier than either grew to become specific circumstances of (co)homology with arbitrary coefficients.

The first chapters of this publication might function a foundation for a graduate-level introductory direction to (co)homology. Simplicial and singular mod 2 (co)homology are brought, with their items and Steenrod squares, in addition to equivariant cohomology. Classical purposes contain Brouwer's mounted element theorem, Poincaré duality, Borsuk-Ulam theorem, Hopf invariant, Smith concept, Kervaire invariant, and so forth. The cohomology of flag manifolds is taken care of intimately (without spectral sequences), together with the connection among Stiefel-Whitney sessions and Schubert calculus. more moderen advancements also are coated, together with topological complexity, face areas, equivariant Morse concept, conjugation areas, polygon areas, among others. each one bankruptcy ends with workouts, with a few tricks and solutions on the finish of the book.

Show description

Read Online or Download Mod Two Homology and Cohomology (Universitext) PDF

Similar geometry & topology books

Geometry II (Universitext)

This can be the second one of a two-volume textbook that gives a really readable and vigorous presentation of enormous components of geometry within the classical feel. for every subject the writer provides a theorem that's esthetically unique and simply said, even supposing the facts will be particularly demanding and hid. one more powerful trait of the ebook is that it presents a entire and unified reference resource for the sphere of geometry within the complete breadth of its subfields and ramifications.

A Panoramic View of Riemannian Geometry

This publication introduces readers to the residing issues of Riemannian Geometry and information the most effects recognized so far. the implications are said with out specific proofs however the major principles concerned are defined, affording the reader a sweeping panoramic view of just about everything of the sphere. From the studies "The ebook has intrinsic price for a pupil in addition to for an skilled geometer.

Deformations of Surface Singularities: 23 (Bolyai Society Mathematical Studies)

The current e-book features a exact number of learn and assessment articles on deformations of floor singularities, that prepare function an introductory survey of effects and strategies of the idea, in addition to open difficulties and examples.  The target is to assemble fabric that may support mathematicians already operating or wishing to paintings during this quarter to deepen their perception and do away with the technical obstacles during this studying approach.

Riemannian Geometry (Graduate Texts in Mathematics)

Meant for a three hundred and sixty five days direction, this article is newly up to date for Kindle and serves as a unmarried resource, introducing readers to the $64000 thoughts and theorems, whereas additionally containing sufficient heritage on complex issues to entice these scholars wishing to focus on Riemannian geometry. this is often one of many few Works to mix either the geometric components of  Riemannian geometry and the analytic features of the idea.

Extra info for Mod Two Homology and Cohomology (Universitext)

Example text

Download PDF sample

Rated 4.33 of 5 – based on 34 votes