In 2009 T.-J. Li and W. Zhang defined an almost complex structure J on a manifold X to be C^\infty-pure-and-full if the second de Rham cohomology group can be decomposed as a direct sum of the subgroups whose elements are cohomology classes admitting J-invariant and J-anti-invariant representatives. It turns out (see T. Draghici, T.-J. Li and W. Zhang (2010)) that any almost complex structure on a 4-dimensional compact manifold is C^\infty-pure-and-full. We study the J-invariant and J-anti-invariant cohomology subgroups on almost complex manifolds, possibly non-compact. In particular, we prove an analytic continuation result for anti-invariant forms on almost complex manifolds. - See more at: http://www.ams.org/journals/proc/2014-142-11/S0002-9939-2014-11578-4/#sthash.yZn8gAfE.dpuf

On non-pure forms on almost complex manifolds / R., Hind; Medori, Costantino; Tomassini, Adriano. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 142:11(2014), pp. 3909-3922. [10.1090/S0002-9939-2014-11578-4]

### On non-pure forms on almost complex manifolds

#### Abstract

In 2009 T.-J. Li and W. Zhang defined an almost complex structure J on a manifold X to be C^\infty-pure-and-full if the second de Rham cohomology group can be decomposed as a direct sum of the subgroups whose elements are cohomology classes admitting J-invariant and J-anti-invariant representatives. It turns out (see T. Draghici, T.-J. Li and W. Zhang (2010)) that any almost complex structure on a 4-dimensional compact manifold is C^\infty-pure-and-full. We study the J-invariant and J-anti-invariant cohomology subgroups on almost complex manifolds, possibly non-compact. In particular, we prove an analytic continuation result for anti-invariant forms on almost complex manifolds. - See more at: http://www.ams.org/journals/proc/2014-142-11/S0002-9939-2014-11578-4/#sthash.yZn8gAfE.dpuf
##### Scheda breve Scheda completa Scheda completa (DC)
On non-pure forms on almost complex manifolds / R., Hind; Medori, Costantino; Tomassini, Adriano. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 142:11(2014), pp. 3909-3922. [10.1090/S0002-9939-2014-11578-4]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2778929
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