# On the real homotopy type of generalized complex nilmanifolds

## TL;DR

This paper demonstrates that in dimensions greater than or equal to 8, there are infinitely many real homotopy types of nilmanifolds with generalized complex structures of all types, contrasting with the limited 6-dimensional case.

## Contribution

It establishes the existence of infinitely many real homotopy types of nilmanifolds with generalized complex structures in higher dimensions, expanding understanding of their diversity.

## Key findings

- Infinite real homotopy types in higher dimensions
- Existence of generalized complex structures of all types
- Contrast with limited 6-dimensional cases

## Abstract

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