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arXiv:1201.4887 [math.DG]AbstractReferencesReviewsResources

Local classification of generalized complex structures

Michael Bailey

Published 2012-01-23, updated 2013-08-05Version 4

We give a local classification of generalized complex structures. About a point, a generalized complex structure is equivalent to a product of a symplectic manifold with a holomorphic Poisson manifold. We use a Nash-Moser type argument in the style of Conn's linearization theorem.

Comments: 29 pages, adapted from Ph.D. thesis; v2 changes: retitled, shortened abstract, corrected typos, changed formatting; v3 changes: equation (2.9) was missing a term, proof of Lemma 6.9 adjusted to accommodate; v4 changes: slight editing, closer to published version
Journal: J. Differential Geom., vol. 95, no. 1 (2013) 1-37
Categories: math.DG, math.SG
Subjects: 53D18
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