A survey of homotopy nilpotency and co-nilpotency

Pracì Mìžnarodnogo Geometričnogo Centru

Marek Golasinski¹ 

[1] University of Warmia and Mazury;

关键词: classical lie group;    h -fibration;    flag manifold;    (oriented) grassmann manifold;    homogenous space;    homology decomposition;    homotopy nilpotency (co-nilpotency) class;    h -space;    h0-space;    n-fold commutator (co-commutator) map;    p-localization;    loop space;    morava k-theory;    postnikov system;    projective space;    sphere;    stiefel manifold;    suspension space;    smash product;   

DOI  :  10.15673/tmgc.v13i4.1750

来源: DOAJ

【 摘 要 】

We review known and state some new results on homotopy nilpotency and co-nilpotency of spaces. Next, we take up the systematic study of homotopy nilpotency of homogenous spaces G/K for a Lie group G and its closed subgroup K < G. The homotopy nilpotency of the loop spaces Ω(Gn,m(K)) and Ω(Vn,m(K)) of Grassmann Gn,m(K) and Stiefel Vn,m(K) manifolds for K = R, C, the field of reals or complex numbers and H, the skew R-algebra of quaternions is shown.

【 授权许可】

Unknown