Let 6/P be a homogenous space with G a compact connected Lie group and P a connected subgroup of G of equal rank. As the rational cohomology ring of G/P is concentrated in even dimen- sions, for an integer k we can de...Let 6/P be a homogenous space with G a compact connected Lie group and P a connected subgroup of G of equal rank. As the rational cohomology ring of G/P is concentrated in even dimen- sions, for an integer k we can define the Adams map of type k to be lk ： H^＊（G/P,Q）→ H^＊（G/P,Q）, lk（u） = k^iu, u ∈ H^2i（G/P,Q）. We show that if k is prime to the order of the Weyl group of G2 then lk can be induced by a self map of G/P. We also obtain results which imply the condition that k is prime to the order of the Weyl group of G is necessary.展开更多
In this paper the classification of maps from a simply connected space X to a flag manifold G/T is studied.As an application,the structure of the homotopy set for self-maps of flag manifolds is determined.
文摘Let 6/P be a homogenous space with G a compact connected Lie group and P a connected subgroup of G of equal rank. As the rational cohomology ring of G/P is concentrated in even dimen- sions, for an integer k we can define the Adams map of type k to be lk ： H^＊（G/P,Q）→ H^＊（G/P,Q）, lk（u） = k^iu, u ∈ H^2i（G/P,Q）. We show that if k is prime to the order of the Weyl group of G2 then lk can be induced by a self map of G/P. We also obtain results which imply the condition that k is prime to the order of the Weyl group of G is necessary.
基金Supported by Chinese Post-Doctoral Scientific Foundation
文摘In this paper the classification of maps from a simply connected space X to a flag manifold G/T is studied.As an application,the structure of the homotopy set for self-maps of flag manifolds is determined.
