On the invariant and anti-invariant cohomologies of hypercomplex manifolds

Mehdi Lejmi, Nicoletta Tardini

A hypercomplex structure $(I,J,K)$ on a manifold $M$ is said to be $C^{\infty }$-pure-and-full if the Dolbeault cohomology $H_{\partial }^{2,0}(M,I)$ is the direct sum of two natural s…