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 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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1-17 |
| Number of pages | 17 |
| Journal | International Mathematics Research Notices |
| Volume | 2010 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2010 |
Bibliographical note
Funding Information:We appreciate V. Apostolov for his very useful comments, R. Hind and T. Perutz for their interest, A. Fino and A. Tomassini for sending us their paper [6], and National Science Foundation for the partial support. We also thank the referees for their careful reading of the manuscript and useful remarks.