Cohomology algebra of mapping spaces between quaternion Grassmannians
Let Gk,n(ℍ) for 2≤k<n denote the quaternion Grassmann manifold of k-dimensional vector subspaces of ℍn. In this paper we compute, in terms of the Sullivan models, the rational cohomology algebra of the component of the inclusion i: Gk,n(ℍ) → Gk,n+r(ℍ) in the space of mappings from Gk,n(ℍ) to Gk,n...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Odesa National University of Technology
2023-08-01
|
| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
| Subjects: | |
| Online Access: | https://journals.ontu.edu.ua/index.php/geometry/article/view/2453 |
| Summary: | Let Gk,n(ℍ) for 2≤k<n denote the quaternion Grassmann manifold of k-dimensional vector subspaces of ℍn. In this paper we compute, in terms of the Sullivan models, the rational cohomology algebra of the component of the inclusion i: Gk,n(ℍ) → Gk,n+r(ℍ) in the space of mappings from Gk,n(ℍ) to Gk,n+r(ℍ) for r≥1 and, more generally, we show that the cohomology of Map(Gk,n(ℍ),Gk,n+r(ℍ);i) contains a truncated algebra ℚ[x]x4r+n+k^{2}-nk for n≥4. |
|---|---|
| ISSN: | 2072-9812 2409-8906 |