Inequalities Frölicher and cohomological decompositions

  • Daniele Angella

    Scuola Normale Superiore, Pisa, Italy
  • Adriano Tomassini

    Università degli Studi di Parma, Italy

Abstract

We study Bott-Chern and Aeppli cohomologies of a vector space endowed with two anti-commuting endomorphisms whose square is zero. In particular, we prove an inequality à la Frölicher relating the dimensions of the Bott-Chern and Aeppli cohomologies to the dimensions of the Dolbeault cohomologies. We prove that the equality in such an inequality à la Frölicher characterizes the validity of the so-called cohomological property of satisfying the -Lemma. As an application, we study cohomological properties of compact either complex, or symplectic, or, more in general, generalized-complex manifolds.

Cite this article

Daniele Angella, Adriano Tomassini, Inequalities Frölicher and cohomological decompositions. J. Noncommut. Geom. 9 (2015), no. 2, pp. 505–542

DOI 10.4171/JNCG/199