On the Real Homotopy Type of Generalized Complex Nilmanifolds

Abstract

We prove that for any n≥4, there are infinitely many real homotopy types of 2n-dimensional nilmanifolds admitting generalized complex structures of every type k, for 0≤k≤n.

Keywords

• nilmanifold
• nilpotent Lie algebra
• complex structure
• symplectic form
• generalized complex structure
• homotopy theory