Torus Actions, Moment Maps, and the Symplectic Geometry of the Moduli Space of Flat Connections on a Two-Manifold. Jeffrey, L. C. & Weitsman, J. In Low-Dimensional Topology and Quantum Field Theory, of NATO ASI Series, pages 307–316. Springer US, Boston, MA, 1993. ![Torus Actions, Moment Maps, and the Symplectic Geometry of the Moduli Space of Flat Connections on a Two-Manifold [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex We summarize recent work ([W],[JW91a], [JW92]) on the symplectic geometry of the moduli space of flat connections on a two-manifold. This work is based on the existence in these moduli spaces of Hamiltonian torus actions. Using these torus actions and the images of the corresponding moment maps we find a simple description of the moduli spaces, and show how it can be used to compute symplectic volumes and other quantities arising in the geometry and topology of the moduli space.
@incollection{jeffrey_torus_1993,
address = {Boston, MA},
series = {{NATO} {ASI} {Series}},
title = {Torus {Actions}, {Moment} {Maps}, and the {Symplectic} {Geometry} of the {Moduli} {Space} of {Flat} {Connections} on a {Two}-{Manifold}},
isbn = {978-1-4899-1612-9},
url = {https://doi.org/10.1007/978-1-4899-1612-9_28},
abstract = {We summarize recent work ([W],[JW91a], [JW92]) on the symplectic geometry of the moduli space of flat connections on a two-manifold. This work is based on the existence in these moduli spaces of Hamiltonian torus actions. Using these torus actions and the images of the corresponding moment maps we find a simple description of the moduli spaces, and show how it can be used to compute symplectic volumes and other quantities arising in the geometry and topology of the moduli space.},
language = {en},
urldate = {2019-06-22},
booktitle = {Low-{Dimensional} {Topology} and {Quantum} {Field} {Theory}},
publisher = {Springer US},
author = {Jeffrey, Lisa C. and Weitsman, Jonathan},
editor = {Osborn, Hugh},
year = {1993},
doi = {10.1007/978-1-4899-1612-9_28},
keywords = {Modulus Space, Riemann Surface, Symplectic Form, Symplectic Manifold, Toric Variety},
pages = {307--316}
}
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