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arXiv · 1908.03016

On the Anti-Invariant Cohomology of Almost Complex Manifolds

Richard Hind·Adriano Tomassini
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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 $\R^4$, 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.

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Richard Hind, Adriano Tomassini. 2019-08-08. On the Anti-Invariant Cohomology of Almost Complex Manifolds. https://arxiv.org/abs/1908.03016

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