✦ LIBER ✦

Some Remarks on Almost and Stable Almost Complex Manifolds

✍ Scribed by Anand Dessai

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 709 KB
Volume: 192
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19981920109

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✦ Synopsis

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 H 1 ( M ; Z) = 0 and no 2-torsion in H i ( M ; Z) 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 f-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.

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