The Resource Introductory Lectures on Equivariant Cohomology : (AMS-204), Loring W. Tu, (electronic resource)
Introductory Lectures on Equivariant Cohomology : (AMS-204), Loring W. Tu, (electronic resource)
Resource Information
The item Introductory Lectures on Equivariant Cohomology : (AMS-204), Loring W. Tu, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Bowdoin College Library.This item is available to borrow from 1 library branch.
Resource Information
The item Introductory Lectures on Equivariant Cohomology : (AMS-204), Loring W. Tu, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Bowdoin College Library.
This item is available to borrow from 1 library branch.
- Summary
- 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
- Language
-
- eng
- eng
- Extent
- 1 online resource (200 p.)
- Contents
-
- 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
- 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
- Isbn
- 9780691197487
- Label
- Introductory Lectures on Equivariant Cohomology : (AMS-204)
- Title
- Introductory Lectures on Equivariant Cohomology
- Title remainder
- (AMS-204)
- Statement of responsibility
- Loring W. Tu
- Language
-
- eng
- eng
- Summary
- 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
- Cataloging source
- DE-B1597
- http://library.link/vocab/creatorName
- Tu, Loring W
- Government publication
- other
- Language note
- In English
- Nature of contents
- dictionaries
- Series statement
- Annals of Mathematics Studies
- Series volume
- 204
- http://library.link/vocab/subjectName
-
- Cohomology operations
- Homology theory
- Target audience
- specialized
- Label
- Introductory Lectures on Equivariant Cohomology : (AMS-204), Loring W. Tu, (electronic resource)
- Contents
-
- 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
- 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
- Control code
- ssj0002346969
- Dimensions
- unknown
- Extent
- 1 online resource (200 p.)
- Form of item
- online
- Governing access note
- Access restricted to subscribing institutions
- Isbn
- 9780691197487
- Lccn
- 2019048303
- Other control number
- 10.1515/9780691197487
- Other physical details
- 37 b/w illus
- Specific material designation
- remote
- System control number
- (WaSeSS)ssj0002346969
- System details
- Mode of access: Internet via World Wide Web
- Label
- Introductory Lectures on Equivariant Cohomology : (AMS-204), Loring W. Tu, (electronic resource)
- Contents
-
- 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
- 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
- Control code
- ssj0002346969
- Dimensions
- unknown
- Extent
- 1 online resource (200 p.)
- Form of item
- online
- Governing access note
- Access restricted to subscribing institutions
- Isbn
- 9780691197487
- Lccn
- 2019048303
- Other control number
- 10.1515/9780691197487
- Other physical details
- 37 b/w illus
- Specific material designation
- remote
- System control number
- (WaSeSS)ssj0002346969
- System details
- Mode of access: Internet via World Wide Web
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.bowdoin.edu/portal/Introductory-Lectures-on-Equivariant-Cohomology-/AQl7crokZA8/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bowdoin.edu/portal/Introductory-Lectures-on-Equivariant-Cohomology-/AQl7crokZA8/">Introductory Lectures on Equivariant Cohomology : (AMS-204), Loring W. Tu, (electronic resource)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bowdoin.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="https://link.bowdoin.edu/">Bowdoin College Library</a></span></span></span></span></div>
