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Tu, Loring W.

Introductory Lectures on Equivariant Cohomology

(AMS-204)

Series:Annals of Mathematics Studies 204

PRINCETON UNIVERSITY PRESS

    269,95 € / $309.50 / £255.00*

    eBook (PDF)
    Publication Date:
    2020
    Copyright year:
    2020
    To be published:
    March 2020
    ISBN
    978-0-691-19748-7
    See all formats and pricing

    Overview

    Aims and Scope

    This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah-Bott and Berline-Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics.

    Assuming readers have taken one semester of manifold theory and a year of algebraic topology, Loring Tu begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localization theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study.

    Details

    200 pages
    37 b/w illus.
    PRINCETON UNIVERSITY PRESS
    Language:
    English
    Readership:
    Professional and scholarly;College/higher education;

    More ...

    Loring W. Tu is professor of mathematics at Tufts University. He is the author of An Introduction to Manifolds and Differential Geometry, and the coauthor (with Raoul Bott) of Differential Forms in Algebraic Topology.

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