國立高雄大學圖資館 |

Language: English

Back

Hamiltonian group actions and equiva...

Dwivedi, Shubham.

Hamiltonian group actions and equivariant cohomology

Record Type:	Electronic resources : Monograph/item
Title/Author:	Hamiltonian group actions and equivariant cohomologyby Shubham Dwivedi ... [et al.].
other author:	Dwivedi, Shubham.
Published:	Cham :Springer International Publishing :2019.
Description:	xi, 132 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Symplectic geometry.
Online resource:	https://doi.org/10.1007/978-3-030-27227-2
ISBN:	9783030272272$q(electronic bk.)

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$q(electronic bk.)

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

468678
Symplectic geometry.

LC Class. No.: QA665

Dewey Class. No.: 516.36

Hamiltonian group actions and equivariant cohomology
LDR:02405nmm a2200337 a 4500 001 566464
003 DE-He213
005 20191223162602.0
006 m d
007 cr nn 008maaau
008 200429s2019 gw s 0 eng d
020 $a 9783030272272$q(electronic bk.)
020 $a 9783030272265$q(paper)
024 7 $a 10.1007/978-3-030-27227-2 $2 doi
035 $a 978-3-030-27227-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA665
072 7 $a PBP $2 bicssc
072 7 $a MAT038000 $2 bisacsh
072 7 $a PBP $2 thema
082 0 4 $a 516.36 $2 23
090 $a QA665 $b .H222 2019
245 0 0 $a Hamiltonian group actions and equivariant cohomology $h [electronic resource] / $c by Shubham Dwivedi ... [et al.].
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xi, 132 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8198
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 468678
650 0 $a Homology theory. $3 205880
650 1 4 $a Topology. $3 185965
650 2 4 $a Geometry. $3 183883
700 1 $a Dwivedi, Shubham. $3 852179
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in mathematics. $3 558795
856 4 0 $u https://doi.org/10.1007/978-3-030-27227-2
950 $a Mathematics and Statistics (Springer-11649)