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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 actio ... More

*Keywords: *
equivariant cohomology,
algebraic topology,
spaces,
smooth manifolds,
differential forms,
equivariant de Rham theorem,
equivariant localization theorem,
circle action

Print publication date: 2020 | Print ISBN-13: 9780691191751 |

Published to Princeton Scholarship Online: January 2021 | DOI:10.23943/princeton/9780691191751.001.0001 |

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## Front Matter

## Part IV Borel Localization

## Part V The Equivariant Localization Formula

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