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Torus actions, moment maps, and the symplectic geometry of the moduli space of flat connections on a two-manifold. (English) Zbl 0811.53028
Sally, Paul J. jun. (ed.) et al., Mathematical aspects of conformal and topological field theories and quantum groups. AMS-IMS-SIAM summer research conference, June 13-19, 1992, Mount Holyoke College, South Hadley, MA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 175, 149-159 (1994).
Summary: We summarize recent work [the second author, Commun. Math. Phys. 145, No. 3, 425-433 (1992; Zbl 0765.53021), the authors, ibid. 150, No. 3, 593-630 (1992; Zbl 0787.53068), and Adv. Math. 106, No. 2, 151-168 (1994)] on the symplectic geometry of the moduli space of flat SU(2) connections on a two-manifold. In this work we exploit 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 space; this description can be used to compute symplectic volumes and other quantities arising in the geometry and topology of the moduli space.
For the entire collection see [Zbl 0801.00049].
MSC:
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
58D27 Moduli problems for differential geometric structures
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