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Hamiltonian group actions and equiva...

Dwivedi, Shubham.

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Hamiltonian group actions and equivariant cohomology

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Hamiltonian group actions and equivariant cohomology/ by Shubham Dwivedi ... [et al.].
其他作者:	Dwivedi, Shubham.
出版者:	Cham :Springer International Publishing : : 2019.,
面頁冊數:	xi, 132 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Symplectic geometry. -
電子資源:	https://doi.org/10.1007/978-3-030-27227-2
ISBN:	9783030272272

Hamiltonian group actions and equivariant cohomology
Hamiltonian group actions and equivariant cohomology[electronic resource] /by Shubham Dwivedi ... [et al.]. - Cham :Springer International Publishing :2019. - xi, 132 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

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.

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.

ISBN: 9783030272272

Standard No.: 10.1007/978-3-030-27227-2doiSubjects--Topical Terms:

752097
Symplectic geometry.

LC Class. No.: QA665

Dewey Class. No.: 516.36

Hamiltonian group actions and equivariant cohomology
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505 0 $a 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.
520 $a 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.
650 0 $a Symplectic geometry. $3 752097
650 0 $a Homology theory. $3 555733
650 1 4 $a Topology. $3 522026
650 2 4 $a Geometry. $3 517251
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