Rational cohomology algebra of mapping spaces between complex Grassmannians
type: Item
instance of: scholarly article
title: Rational cohomology algebra of mapping spaces between complex Grassmannians
zbMATH Open document ID: 1486.55017
DOI: 10.1155/2020/9385153
author: Paul Antony Otieno
author: Vitalis Onyango-Otieno
author: Jean Baptiste Gatsinzi
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2020-04-24T00:00:00Z
review text: Summary: We consider the complex Grassmannian \(\mathrm{Gr} (k, n)\) of \(k\)-dimensional subspaces of \(\mathbb{C}^n\). There is a natural inclusion \(i_{n, r} : \mathrm{Gr} (k, n) \hookrightarrow \mathrm{Gr} (k, n + r)\). Here, we use Sullivan models to compute the rational cohomology algebra of the component of the inclusion \(i_{n, r}\) in the space of mappings from \(\mathrm{Gr} (k, n)\) to \(\mathrm{Gr} (k, n + r)\) for \(r \geq 1\) and in particular to show that the cohomology of \(\text{map} (\mathrm{Gr} (n, k), \mathrm{Gr} (n, k + r); i_{n, r})\) contains a truncated algebra \(\mathbb{Q} [x] / x^{r + n + k^2 - n k} \), where \(|x| = 2\), for \(k \geq 2\) and \(n \geq 4\).
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 55P15
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 55R10
zbMATH DE Number: 7193178
zbMATH Keywords: complex Grassmannian
zbMATH Keywords: Sullivan models
zbMATH Keywords: cohomology algebra
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/9385153
OpenAlex ID: W3004038033
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description: scientific article; zbMATH DE number 7193178