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Locally toric manifolds and singular Bohr-Sommerfeld leaves
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eBook
Locally toric manifolds and singular Bohr-Sommerfeld leaves
2010
Overview
When geometric quantization is applied to a manifold using a real polarization which is “nice enough”, a result of Śniatycki says
that the quantization can be found by counting certain objects, called Bohr-Sommerfeld leaves. Subsequently, several authors have taken
this as motivation for counting Bohr-Sommerfeld leaves when studying the quantization of manifolds which are less “nice”.
In this
paper, we examine the quantization of compact symplectic manifolds that can locally be modelled by a toric manifold, using a real
polarization modelled on fibres of the moment map. We compute the results directly, and obtain a theorem similar to Śniatycki’s, which
gives the quantization in terms of counting Bohr-Sommerfeld leaves. However, the count does not include the Bohr-Sommerfeld leaves which
are singular. Thus the quantization obtained is different from the quantization obtained using a Kähler polarization.
Publisher
American Mathematical Society
Subject
ISBN
9780821847145, 0821847147
