TY - JOUR

T1 - Rational Cohomology Algebra of Mapping Spaces between Complex Grassmannians

AU - Otieno, Paul Antony

AU - Gatsinzi, Jean Baptiste

AU - Onyango-Otieno, Vitalis

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - https://www.mendeley.com/catalogue/651a1daf-8383-385b-a54a-d91f69353c47/

U2 - 10.1155/2020/9385153

DO - 10.1155/2020/9385153

M3 - Article

VL - 2020

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

M1 - 9385153

ER -