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Title: Calculus on symplectic manifolds (English)
Author: Eastwood, Michael
Author: Slovák, Jan
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 54
Issue: 5
Year: 2018
Pages: 265-280
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: symplectic structure
Keyword: Kähler structure
Keyword: tractor calculus
Keyword: exact complex
Keyword: BGG machinery
MSC: 53B35
MSC: 53D05
idZBL: Zbl 06997355
idMR: MR3887354
DOI: 10.5817/AM2018-5-265
Date available: 2018-12-06T16:14:04Z
Last updated: 2020-01-05
Stable URL:
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