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arXiv · 1709.03059

Calculus on symplectic manifolds

Michael Eastwood·Jan Slovak
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Abstract

On a symplectic manifold, there is a natural elliptic complex replacing the de Rham complex. It can be coupled to a vector bundle with connection and, when the curvature of this connection is constrained to be a multiple of the symplectic form, we find a new complex. In particular, on complex projective space with its Fubini-Study form and connection, we can build a series of differential complexes akin to the Bernstein-Gelfand-Gelfand complexes from parabolic differential geometry.

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Michael Eastwood, Jan Slovak. 2017-09-10. Calculus on symplectic manifolds. https://arxiv.org/abs/1709.03059

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