On the geometry of prequantization spaces

Details On the geometry of prequantization spaces On the geometry of prequantization spaces

2005-11-07

arxiv.org/abs/math/0511187v2

J. of Geom. and Physics, Vol. 57, Issue 11 (Oct. 2007), pp. 2372-2397.

Mathematics

Differential Geometry

29 pages

Scientific paper

Given a Poisson (or more generally Dirac) manifold $P$, there are two approaches to its geometric quantization: one involves a circle bundle $Q$ over $P$ endowed with a Jacobi (or Jacobi-Dirac) structure; the other one involves a circle bundle with a (pre-) contact groupoid structure over the (pre-) symplectic groupoid of $P$. We study the relation between these two prequantization spaces. We show that the circle bundle over the (pre-) symplectic groupoid of $P$ is obtained from the groupoid of $Q$ via an $S^1$ reduction that preserves both the groupoid and the geometric structure.

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