In many applications of Lie group theory, one needs detailed information on the homotopy invariants of Lie groups. By the theorem of Mal'tsev-Iwasawa, it suffices to look at compact Lie groups. Compact Lie groups are subdirect products of tori and compact quasisimple Lie groups, and the ...
In many applications of Lie group theory, one needs detailed information on the homotopy invariants of Lie groups. By the theorem of Mal'tsev-Iwasawa, it suffices to look at compact Lie groups. Compact Lie groups are subdirect products of tori and compact quasisimple Lie groups, and the latt...
The p-adic reflection groups play an important rôle in the theory of so-called p-compact groups, which constitute a homotopy theoretic analogue of compact Lie groups. By definition, a p-compact group is a p-complete topological space BX such that the homology H*(X;Fp) of the loop spac...
The group of homotopy equivalences of products of spheres and of Lie groups - Arkowitz, StromM. Arkowitz and J. Strom. The group of homotopy equivalences of products of spheres and of Lie groups. preprint.M. Arkowitz, J. Strom, The group of homotopy equivalences of products of spheres ...
S Deng, S Deng - Homogeneous Finsler Spaces, 2012 - link.springer.com Mann, L., Sicks, J., Su, J.: The degree of symmetry of a homotopy real projective space. 49,232–244 (1974); Li, B., Shen, Z.: On projectively flat fourth root metrics. Kluwer Academic,Dordrecht (2001); ...
摘要: We show that if G is a compact connected Lie group that has p-torsion in homology, then G localized at p is not homotopy nilpotent. Thus, a connected Lie group is homotopy nilpotent if and only if it has no torsion in homology....
Homotopy Nilpotency Introduction Main Theorem Definitions Motive Work Definitions Homotopy Nilpotency X: topological group. iterated commutator map γ n : n+1 X →X. γ 1 = γ : (x, y) →xyx −1 y −1 , γ n = γ ◦ (1 ∧γ n−1 ). homotopy nilpotency of X [...
给出一个以G/H为底空间， 所有fibers 同胚于H的fiber bundle, 而fiber bundles 是 homotopy fiber ...
We study a filtration on the group of homotopy classes of self maps of a compact Lie group associated with homotopy groups. We determine these filtrations of SU(3) and Sp(2) completely. We introduce two natural invariants $lz_p(X)$ and $sz_p(X)$ defined by the filtration, where p ...
Hellen Colman. On the 1-homotopy type of Lie groupoids. Applied Categorical Structures, 19(1):393-423, 2011.On the 1-homotopy type of Lie groupoids - Colman () Citation Context ...A Morita homotopy equivalence K ≃ G induces a Morita equivalence between the homotopy groupoids K ∗...