Geometric quantization of semitoric systems and almost toric manifolds
Tipus de documentReport de recerca
Data publicació2017
Condicions d'accésAccés obert
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Abstract
Kostant gave a model for the real geometric quantization
associated to polarizations via the cohomology associated to the sheaf of
flat sections of a pre-quantum line bundle. This model is well-adapted
for real polarizations given by integrable systems and toric manifolds.
In the latter case, the cohomology can be computed counting integral
points inside the associated Delzant polytope. In this article we extend
Kostant’s geometric quantization to semitoric integrable systems and
almost toric manifolds. In these cases the dimension of the acting torus
is smaller than half of the dimension of the manifold. In particular, we
compute the cohomology groups associated to the geometric quantization
if the real polarization is the one associated to an integrable system
with focus-focus type singularities in dimension four. As application
we determine models for the geometric quantization of K3 surfaces, a
spin-spin system, the spherical pendulum, and a spin-oscillator system
under this scheme.
CitacióMiranda, E., Presas, F., Solha, R. "Geometric quantization of semitoric systems and almost toric manifolds". 2017.
URL repositori externhttps://arxiv.org/pdf/1705.06572.pdf
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1705.06572.pdf | 288,2Kb | Visualitza/Obre | ||
finalMirandaPresasSolha.pdf | 444,8Kb | Visualitza/Obre |