Introductory lectures on equivariant cohomology / Loring W. Tu.

Format:

Book

Author/Creator:

Tu, Loring W., author.

Contributor:

Arabia, Alberto, contributor.

Series:

Annals of mathematics studies ; number 204.

Princeton scholarship online.

Annals of mathematics studies ; number 204

Princeton scholarship online

Language:

English

Subjects (All):

Cohomology operations.

Physical Description:

1 online resource (338 pages)

Place of Publication:

Princeton : Princeton University Press, 2021.

Language Note:

In English.

Summary:

This volume gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. 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 localisation 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.

Contents:

Frontmatter

Contents

List of Figures

Preface

Acknowledgments

Part I. Equivariant Cohomology in the Continuous Category

Part II. Differential Geometry of a Principal Bundle

Part III. The Cartan Model

Part IV. Borel Localization

Part V. The Equivariant Localization Formula

Appendices

Hints and Solutions to Selected End-of-Section Problems

List of Notations

Bibliography

Index

Notes:

Description based on online resource; title from home page (viewed on December 17, 2020).

Previously issued in print: 2020.

Includes bibliographical references and index.

ISBN:

9780691197487

0691197482

OCLC:

1147841610