Prequantization of the Moduli Space of Flat PU(p) -Bundles with Prescribed Boundary Holonomies

Krepski, Derek

doi:10.3842/sigma.2014.109

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Applications To 2-plectic and Quasi-hamiltonian Geometry1

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2020

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“…A prequantization of a quasi-Hamiltonian G-space (M, ω, Φ) is a relative G-equivariant bundle gerbe (Q, G) for Φ-i. For related work on the integrality conditions required for prequantization of the moduli space of flat Gbundles, see [19,20,22,25].…”

Section: Applications To 2-plectic and Quasi-hamiltonian Geometrymentioning

confidence: 99%

Multiplicative vector fields on bundle gerbes

Krepski,

Vaughan

2020

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This paper makes use of multiplicative vector fields on Lie groupoids to model infinitesimal symmetries of S 1 -bundle gerbes. It is shown that a connective structure on a bundle gerbe gives rise to a natural horizontal lift of multiplicative vector fields to the bundle gerbe, and that the 3-curvature presents the obstruction to the horizontal lift being a morphism of Lie 2-algebras. Connectionpreserving multiplicative vector fields on a bundle gerbe with connective structure are shown to inherit a natural Lie 2-algebra structure; moreover, this Lie 2-algebra is quasi-isomorphic to the Poisson-Lie 2-algebra of the 2-plectic base manifold (M, χ), where χ is the 3-curvature of the connective structure. As an application of this result, we give an analogue of a formula of Kostant in the 2-plectic and quasi-Hamiltonian context.

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Section: Applications To 2-plectic and Quasi-hamiltonian Geometrymentioning

confidence: 99%