Title: Symplectic Forms and Cohomology Decomposition of almost Complex Four-Manifolds
Abstract:For any compact almost complex manifold (M, J), the last two authors [8] defined two subgroups H+J(M), H−J(M) of the degree 2 real de Rham cohomology group . These are the sets of cohomology classes ...For any compact almost complex manifold (M, J), the last two authors [8] defined two subgroups H+J(M), H−J(M) of the degree 2 real de Rham cohomology group . These are the sets of cohomology classes which can be represented by J-invariant, respectively, J-antiinvariant real 2-forms. In this paper, it is shown that in dimension 4 these subgroups induce a cohomology decomposition of . This is a specifically four-dimensional result, as it follows from a recent work of Fino and Tomassini [6]. Some estimates for the dimensions of these groups are also established when the almost complex structure is tamed by a symplectic form and an equivalent formulation for a question of Donaldson is given.Read More
Publication Year: 2009
Publication Date: 2009-07-22
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 60
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