Introductory lectures on equivariant cohomology:
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 introduc...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Princeton ; NJ
Princeton University Press
[2020]
|
| Schriftenreihe: | Annals of mathematics studies
Number 204 |
| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FHR01 FKE01 FLA01 TUM01 UBY01 UPA01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | 1 Online-Ressource (xix,200 Seiten) Illustrationen |
| ISBN: | 9780691197487 |
| DOI: | 10.1515/9780691197487 |
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| 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 | ||
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| spelling | Tu, Loring W. 1952- (DE-588)110090322 aut Introductory lectures on equivariant cohomology Loring W. Tu Princeton ; NJ Princeton University Press [2020] © 2020 1 Online-Ressource (xix,200 Seiten) Illustrationen txt rdacontent c rdamedia cr rdacarrier Annals of mathematics studies Number 204 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 In English MATHEMATICS / Geometry / Algebraic bisacsh Homology theory Erscheint auch als Druck-Ausgabe 978-0-691-19174-4 Annals of mathematics studies Number 204 (DE-604)BV040389493 204 https://doi.org/10.1515/9780691197487 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Tu, Loring W. 1952- Introductory lectures on equivariant cohomology Annals of mathematics studies MATHEMATICS / Geometry / Algebraic bisacsh Homology theory |
| title | Introductory lectures on equivariant cohomology |
| title_auth | Introductory lectures on equivariant cohomology |
| title_exact_search | Introductory lectures on equivariant cohomology |
| title_exact_search_txtP | Introductory lectures on equivariant cohomology |
| title_full | Introductory lectures on equivariant cohomology Loring W. Tu |
| title_fullStr | Introductory lectures on equivariant cohomology Loring W. Tu |
| title_full_unstemmed | Introductory lectures on equivariant cohomology Loring W. Tu |
| title_short | Introductory lectures on equivariant cohomology |
| title_sort | introductory lectures on equivariant cohomology |
| topic | MATHEMATICS / Geometry / Algebraic bisacsh Homology theory |
| topic_facet | MATHEMATICS / Geometry / Algebraic Homology theory |
| url | https://doi.org/10.1515/9780691197487 |
| volume_link | (DE-604)BV040389493 |
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