The decomposition of forms and cohomology of generalized complex manifolds

[摘要] We study the decomposition of forms induced by a generalized complex structure giving a complete description of the bundles involved and, around regular points, of the operators a and () associated to the generalized complex structure. We prove that if the generalized partial derivative partial derivative-lemma holds then the decomposition of forms gives rise to a decomposition of the cohomology of the manifold, H-center dot (M) = circle plus(n)(-n) GH(k) (M), and the canonical spectral sequence degenerates at El. We also show that if the generalized partial derivative partial derivative-lemma holds, any generalized complex submanifold can be associated to a Poincare dual cohomology class in the middle cohomology space G H-0(M). (c) 2006 Elsevier B.V. All rights reserved.

[发布日期] 2006-12-31

[关键词] generalized complex geometry;cohomology decomposition