On the J -Anti-invariant cohomology of almost complex 4-manifolds

Tedi Draghici; Tian Jun Li; Weiyi Zhang

doi:10.1093/qmath/har034

On the J -Anti-invariant cohomology of almost complex 4-manifolds

Tedi Draghici, Tian Jun Li, Weiyi Zhang

Mathematics

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Abstract

For a compact almost complex 4-manifold (M, J ), we study the subgroups H^±_J of H² (M,R)consisting of cohomology classes representable by J -invariant, respectively, J -anti-invariant real 2-forms. If b⁺ = 1, we show that, for generic almost complex structures on M, the subgroup H_J is trivial. Computations of the subgroups and their dimensions h^±_J are obtained foralmost complex structures related to integrable ones. We also prove semi-continuity propertiesfor h^±_J.

Original language	English (US)
Pages (from-to)	83-111
Number of pages	29
Journal	Quarterly Journal of Mathematics
Volume	64
Issue number	1
DOIs	https://doi.org/10.1093/qmath/har034
State	Published - Mar 2013

Bibliographical note

Funding Information:
During the preparation of this work, the authors benefited from partial support from NSF grant DMS-0604748 (of the second author).

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abstract = "For a compact almost complex 4-manifold (M, J ), we study the subgroups H±J of H2 (M,R)consisting of cohomology classes representable by J -invariant, respectively, J -anti-invariant real 2-forms. If b+ = 1, we show that, for generic almost complex structures on M, the subgroup HJ is trivial. Computations of the subgroups and their dimensions h±J are obtained foralmost complex structures related to integrable ones. We also prove semi-continuity propertiesfor h±J.",

author = "Tedi Draghici and Li, {Tian Jun} and Weiyi Zhang",

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AU - Li, Tian Jun

AU - Zhang, Weiyi

N1 - Funding Information: During the preparation of this work, the authors benefited from partial support from NSF grant DMS-0604748 (of the second author).

PY - 2013/3

Y1 - 2013/3

N2 - For a compact almost complex 4-manifold (M, J ), we study the subgroups H±J of H2 (M,R)consisting of cohomology classes representable by J -invariant, respectively, J -anti-invariant real 2-forms. If b+ = 1, we show that, for generic almost complex structures on M, the subgroup HJ is trivial. Computations of the subgroups and their dimensions h±J are obtained foralmost complex structures related to integrable ones. We also prove semi-continuity propertiesfor h±J.

AB - For a compact almost complex 4-manifold (M, J ), we study the subgroups H±J of H2 (M,R)consisting of cohomology classes representable by J -invariant, respectively, J -anti-invariant real 2-forms. If b+ = 1, we show that, for generic almost complex structures on M, the subgroup HJ is trivial. Computations of the subgroups and their dimensions h±J are obtained foralmost complex structures related to integrable ones. We also prove semi-continuity propertiesfor h±J.

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On the J -Anti-invariant cohomology of almost complex 4-manifolds

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