### Abstract

The complex Grassmann Gr(k, n) is the space of k dimensional subspaces of ℂ ^{n} . It is a complex manifold of complex dimension k(n − k). There is a natural inclusion i _{k} _{,n} : Gr(k, n) ↪ Gr(k, n + r). In this paper, we use Sullivan models to compute the rational homotopy type of the component of the inclusion Gr(2, n) ↪ Gr(2, n + r) in the space of mappings from Gr(2, n) to Gr(2, n + r), r ≥ 1. We show in particular that map(Gr(2, n), Gr(2, n + 1); i _{n} ) has the rational homotopy type of a product of odd spheres.

Original language | English |
---|---|

Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Quaestiones Mathematicae |

DOIs | |

Publication status | Published - Apr 2019 |

### All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)

## Fingerprint Dive into the research topics of 'Rational homotopy of mapping spaces between complex Grassmannians'. Together they form a unique fingerprint.

## Cite this

*Quaestiones Mathematicae*, 1-12. https://doi.org/10.2989/16073606.2019.1601139