Abstract: | In the first part we give necessary and sufficient conditions for the existence of a stable almost complex structure on a 10-manifold M with H1(M;?) = 0 and no 2-torsion in H1(M;?) for i = 2,3. Using the Classification Theorem of Donaldson we give a reformulation of the conditions for a 4-manifold to be almost complex in terms of Betti numbers and the dimension of the ±-eigenspaces of the intersection form. In the second part we give general conditions for an almost complex manifold to admit infinitely many almost complex structures and apply these to symplectic manifolds, to homogeneous spaces and to complete intersections. |