Hamiltonian Group Actions and Equivariant Cohomology
(Sprache: Englisch)
This monograph could be used for a graduate course on symplectic geometry as well as for independent study.
The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions...
The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions...
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Klappentext zu „Hamiltonian Group Actions and Equivariant Cohomology “
This monograph could be used for a graduate course on symplectic geometry as well as for independent study.The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry.
Inhaltsverzeichnis zu „Hamiltonian Group Actions and Equivariant Cohomology “
Symplectic vector spaces.- Hamiltonian group actions.- The Darboux-Weinstein Theorem.- Elementary properties of moment maps.- The symplectic structure on coadjoint orbits.- Symplectic Reduction.- Convexity.- Toric Manifolds.- Equivariant Cohomology.- The Duistermaat-Heckman Theorem.- Geometric Quantization.- Flat connections on 2-manifolds.
Bibliographische Angaben
- Autoren: Shubham Dwivedi , Jonathan Herman , Lisa C. Jeffrey , Theo van den Hurk
- 2019, 1st ed. 2019, XI, 132 Seiten, 1 farbige Abbildungen, Maße: 16,2 x 26,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3030272265
- ISBN-13: 9783030272265
Sprache:
Englisch
Pressezitat
"The target audience is graduate students; ... this monograph could easily be used by researchers interested in learning the subject at a fast pace. It is a perfect text for a seminar course. ... the book's material is presented in a crisp and abridged manner. ... This makes the presentation short and highly valuable." (Eduardo A. Gonzalez, Mathematical Reviews, December, 2020)
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