##plugins.themes.bootstrap3.article.main##
Abstract
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.
##plugins.themes.bootstrap3.article.details##
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution (CC-BY) 4.0 License that allows others to share the work with an acknowledgment of the work’s authorship and initial publication in this journal.
Provided they are the owners of the copyright to their work, authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal’s published version of the work (e.g., post it to an institutional repository, in a journal or publish it in a book), with an acknowledgment of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories, disciplinary repositories, or on their website) prior to and during the submission process.