Rational Cohomology Algebra of Mapping Spaces between Complex Grassmannians

Paul Antony Otieno, Jean Baptiste Gatsinzi, Vitalis Onyango-Otieno

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We consider the complex Grassmannian Grk,n of k-dimensional subspaces of ℂn. There is a natural inclusion in,r:Grk,n↪Grk,n+r. Here, we use Sullivan models to compute the rational cohomology algebra of the component of the inclusion in,r in the space of mappings from Grk,n to Grk,n+r for r≥1 and in particular to show that the cohomology of mapGrn,k,Grn,k+r;in,r contains a truncated algebra ℚx/xr+n+k2−nk, where x=2, for k≥2 and n≥4.
Original languageEnglish
Article number9385153
Number of pages4
JournalInternational Journal of Mathematics and Mathematical Sciences
Publication statusPublished - 2020


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