Abstract
The chapter begins with a discussion of circle actions and their relation to 2-sphere bundles. It continues with a section on general Hamiltonian group actions and moment maps, then proceeds to discuss various explicit examples in both finite and infinite dimensions, and introduces the Marsden–Weinstein quotient, together with new examples that explain its relation to the construction of generating functions for Lagrangians. Further sections give a proof of the Atiyah–Guillemin–Sternberg convexity theorem about the image of the moment map in the case of torus actions, and use equivariant cohomology to prove the Duistermaat–Heckman localization formula for circle actions. It closes with an overview of geometric invariant theory which grows out of the interplay between the actions of a real Lie group and its complexification.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
