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Introductory lectures on equivariant...

Tu, Loring W.

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Introductory lectures on equivariant cohomology

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Introductory lectures on equivariant cohomology/ Loring W. Tu ; with appendices by Loring W. Tu and Alberto Arabia.
作者:	Tu, Loring W.
其他作者:	Arabia, Alberto.
出版者:	Princeton, NJ :Princeton University Press, : 2020.,
面頁冊數:	1 online resource (338 p.)
標題:	Homology theory. -
電子資源:	https://portal.igpublish.com/iglibrary/search/PUPB0007284.html
ISBN:	9780691197487

Introductory lectures on equivariant cohomology
Tu, Loring W.

Introductory lectures on equivariant cohomology[electronic resource] /Loring W. Tu ; with appendices by Loring W. Tu and Alberto Arabia. - Princeton, NJ :Princeton University Press,2020. - 1 online resource (338 p.) - Annals of mathematics studies ;no. 204. - Annals of mathematics studies ;no. 204..

Includes bibliographical references and index.

Access restricted to authorized users and institutions.

"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"--

Mode of access: World Wide Web.

ISBN: 9780691197487Subjects--Topical Terms:

555733
Homology theory.

LC Class. No.: QA612.3

Dewey Class. No.: 514.23

Introductory lectures on equivariant cohomology
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300 $a 1 online resource (338 p.)
490 1 $a Annals of mathematics studies ; $v no. 204
504 $a Includes bibliographical references and index.
506 $a Access restricted to authorized users and institutions.
520 $a "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"-- $c Provided by publisher.
538 $a Mode of access: World Wide Web.
588 $a Description based on print version record.
650 0 $a Homology theory. $3 555733
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