A Poincare lemma in Geometric Quantisation
Eva Miranda, Romero Solha
TL;DR
This paper establishes a Poincare lemma for the Kostant complex in geometric quantisation, specifically addressing cases with Lagrangian foliations and nondegenerate singularities, aiding in the computation of quantisation.
Contribution
It introduces a Poincare lemma tailored for the Kostant complex in the context of geometric quantisation with singular polarizations.
Findings
Provides a new mathematical tool for geometric quantisation with singularities
Enables computation of quantisation in more complex symplectic manifolds
Extends classical results to cases with nondegenerate singularities
Abstract
This article presents a Poincare lemma for the Kostant complex, used to compute geometric quantisation, when the polarisation is given by a Lagrangian foliation defined by an integrable system with nondegenerate singularities.
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