On the real homotopy type of generalized complex nilmanifolds

Abstract

We prove that for any $n\ge 4$ there are infinitely many real homotopy types of $2n$-dimensional nilmanifolds admitting generalized complex structures of every type $k$, for $0\le k\le n$. This is in deep contrast to the $6$-dimensional case.

11 pages; observation added concerning higher dimensions; change of title and abstract