We study the space of closed anti-invariant forms on an almost complex manifold, possibly non-compact. We construct families of (non-integrable) almost complex structures on R4, such that the space of closed J-anti-invariant forms is infinite dimensional, and also 0- or 1-dimensional. In the compact case, we construct 6-dimensional almost complex manifolds with arbitrary large anti-invariant cohomology and a 2-parameter family of almost complex structures on the Kodaira–Thurston manifold whose anti-invariant cohomology group has maximum dimension.

On the Anti-invariant Cohomology of Almost Complex Manifolds / Hind, R.; Tomassini, A.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 31:5(2021), pp. 4906-4922. [10.1007/s12220-020-00461-8]

On the Anti-invariant Cohomology of Almost Complex Manifolds

Tomassini A.
2021

Abstract

We study the space of closed anti-invariant forms on an almost complex manifold, possibly non-compact. We construct families of (non-integrable) almost complex structures on R4, such that the space of closed J-anti-invariant forms is infinite dimensional, and also 0- or 1-dimensional. In the compact case, we construct 6-dimensional almost complex manifolds with arbitrary large anti-invariant cohomology and a 2-parameter family of almost complex structures on the Kodaira–Thurston manifold whose anti-invariant cohomology group has maximum dimension.
On the Anti-invariant Cohomology of Almost Complex Manifolds / Hind, R.; Tomassini, A.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 31:5(2021), pp. 4906-4922. [10.1007/s12220-020-00461-8]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2911717
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