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
SN - 0161-1712
VL - 2020
JO - International Journal of Mathematics and Mathematical Sciences
JF - International Journal of Mathematics and Mathematical Sciences
M1 - 9385153
ER -