On the Anti-Invariant Cohomology of Almost Complex Manifolds

Richard Hind, Adriano Tomassini

Published 2019-08-08Version 1

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 $\mathbb{R}^4$, such that the space of harmonic $J$-anti-invariant forms is infinite dimensional respectively $1$-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 strcuctures on the Kodaira-Thurston manifold whose anti-invariant cohomology group has maximum dimension.