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Some Remarks on Almost and Stable Almost Complex Manifolds
Author(s) -
Dessai Anand
Publication year - 1998
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19981920109
Subject(s) - mathematics , betti number , pure mathematics , symplectic geometry , complex manifold , manifold (fluid mechanics) , closed manifold , complex dimension , homogeneous , torsion (gastropod) , dimension (graph theory) , combinatorics , invariant manifold , mechanical engineering , holomorphic function , engineering , medicine , surgery
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 1 (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 ±‐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.