Introductory Lectures on Equivariant Cohomology : : (AMS-204) / / Loring W. Tu.
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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Superior document: | Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 English |
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2020] ©2020 |
Year of Publication: | 2020 |
Language: | English |
Series: | Annals of Mathematics Studies ;
204 |
Online Access: | |
Physical Description: | 1 online resource (200 p.) :; 37 b/w illus. |
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LEADER | 08781nam a22020055i 4500 | ||
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035 | |a (OCoLC)1147841610 | ||
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100 | 1 | |a Tu, Loring W., |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Introductory Lectures on Equivariant Cohomology : |b (AMS-204) / |c Loring W. Tu. |
264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2020] | |
264 | 4 | |c ©2020 | |
300 | |a 1 online resource (200 p.) : |b 37 b/w illus. | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a Annals of Mathematics Studies ; |v 204 | |
505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t List of Figures -- |t Preface -- |t Acknowledgments -- |t Part I. Equivariant Cohomology in the Continuous Category -- |t Part II. Differential Geometry of a Principal Bundle -- |t Part III. The Cartan Model -- |t Part IV. Borel Localization -- |t Part V. The Equivariant Localization Formula -- |t Appendices -- |t Hints and Solutions to Selected End-of-Section Problems -- |t List of Notations -- |t Bibliography -- |t Index |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
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. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 27. Jan 2023) | |
650 | 0 | |a Cohomology operations. | |
650 | 7 | |a MATHEMATICS / Geometry / Algebraic. |2 bisacsh | |
653 | |a Algebraic structure. | ||
653 | |a Algebraic topology (object). | ||
653 | |a Algebraic topology. | ||
653 | |a Algebraic variety. | ||
653 | |a Basis (linear algebra). | ||
653 | |a Boundary (topology). | ||
653 | |a CW complex. | ||
653 | |a Cellular approximation theorem. | ||
653 | |a Characteristic class. | ||
653 | |a Classifying space. | ||
653 | |a Coefficient. | ||
653 | |a Cohomology ring. | ||
653 | |a Cohomology. | ||
653 | |a Comparison theorem. | ||
653 | |a Complex projective space. | ||
653 | |a Continuous function. | ||
653 | |a Contractible space. | ||
653 | |a Cramer's rule. | ||
653 | |a Curvature form. | ||
653 | |a De Rham cohomology. | ||
653 | |a Diagram (category theory). | ||
653 | |a Diffeomorphism. | ||
653 | |a Differentiable manifold. | ||
653 | |a Differential form. | ||
653 | |a Differential geometry. | ||
653 | |a Dual basis. | ||
653 | |a Equivariant K-theory. | ||
653 | |a Equivariant cohomology. | ||
653 | |a Equivariant map. | ||
653 | |a Euler characteristic. | ||
653 | |a Euler class. | ||
653 | |a Exponential function. | ||
653 | |a Exponential map (Lie theory). | ||
653 | |a Exponentiation. | ||
653 | |a Exterior algebra. | ||
653 | |a Exterior derivative. | ||
653 | |a Fiber bundle. | ||
653 | |a Fixed point (mathematics). | ||
653 | |a Frame bundle. | ||
653 | |a Fundamental group. | ||
653 | |a Fundamental vector field. | ||
653 | |a Group action. | ||
653 | |a Group homomorphism. | ||
653 | |a Group theory. | ||
653 | |a Haar measure. | ||
653 | |a Homotopy group. | ||
653 | |a Homotopy. | ||
653 | |a Hopf fibration. | ||
653 | |a Identity element. | ||
653 | |a Inclusion map. | ||
653 | |a Integral curve. | ||
653 | |a Invariant subspace. | ||
653 | |a K-theory. | ||
653 | |a Lie algebra. | ||
653 | |a Lie derivative. | ||
653 | |a Lie group action. | ||
653 | |a Lie group. | ||
653 | |a Lie theory. | ||
653 | |a Linear algebra. | ||
653 | |a Linear function. | ||
653 | |a Local diffeomorphism. | ||
653 | |a Manifold. | ||
653 | |a Mathematics. | ||
653 | |a Matrix group. | ||
653 | |a Mayer–Vietoris sequence. | ||
653 | |a Module (mathematics). | ||
653 | |a Morphism. | ||
653 | |a Neighbourhood (mathematics). | ||
653 | |a Orthogonal group. | ||
653 | |a Oscillatory integral. | ||
653 | |a Principal bundle. | ||
653 | |a Principal ideal domain. | ||
653 | |a Quotient group. | ||
653 | |a Quotient space (topology). | ||
653 | |a Raoul Bott. | ||
653 | |a Representation theory. | ||
653 | |a Ring (mathematics). | ||
653 | |a Singular homology. | ||
653 | |a Spectral sequence. | ||
653 | |a Stationary phase approximation. | ||
653 | |a Structure constants. | ||
653 | |a Sub"ient. | ||
653 | |a Subcategory. | ||
653 | |a Subgroup. | ||
653 | |a Submanifold. | ||
653 | |a Submersion (mathematics). | ||
653 | |a Symplectic manifold. | ||
653 | |a Symplectic vector space. | ||
653 | |a Tangent bundle. | ||
653 | |a Tangent space. | ||
653 | |a Theorem. | ||
653 | |a Topological group. | ||
653 | |a Topological space. | ||
653 | |a Topology. | ||
653 | |a Unit sphere. | ||
653 | |a Unitary group. | ||
653 | |a Universal bundle. | ||
653 | |a Vector bundle. | ||
653 | |a Vector space. | ||
653 | |a Weyl group. | ||
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773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2020 English |z 9783110704846 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2020 |z 9783110704662 |o ZDB-23-DMA |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Annals of Mathematics eBook-Package 1940-2020 |z 9783110494914 |o ZDB-23-PMB |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press Complete eBook-Package 2020 |z 9783110690088 |
776 | 0 | |c print |z 9780691191751 | |
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912 | |a 978-3-11-070484-6 EBOOK PACKAGE Mathematics 2020 English |b 2020 | ||
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