Homotopy Lie groups, recently invented by W.G. Dwyer and C.W. Wilkerson, represent the culmination of a long evolution. The basic philosophy behind the process was formulated almost 25 years ago by Rector in his vision of a homotopy theoretic incarnation of Lie group theory. What was then ...
We give a very simple construction of the string 2-group as a strict Fréchet Lie 2-group. The corresponding crossed module is defined using the conjugation action of the loop group on its central extension, which drastically simplifies several constructions previously given in the literature. More...
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); ...
X: homotopy commutative def ⇐⇒nil X = 1. X: homotopy nilpotent def ⇐⇒nil X < ∞. (Hopkins, Rao [Ho],[Ra]) G: compact Lie group G (p) is homotopy nilpotent ⇔H∗(G; Z) has no p-torsion. Homotopy Nilpotency Introduction Main Theorem Definitions Motive Work Defi...
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...
Homotopy Theory of Lie Groups , homotopy normality and nilpotency, and on the trivialization of the tangent bundle obtained from the group multiplication. For proofs and a more detailed exposition, compare also [the author and H. Toda, Topology of Lie groups I ......
1.5.4 A general connected Lie group 1.5.5 The general metric B–NB classification 1.5.6 The drawback of this metric classification 1.6 Homotopy Retracts 1.6.1 The classical retract 1.6.2 The polynomial retract 1.6.3 The polynomial retract property used in the B–NB classification ...
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....
the same Poincar´e polynomial, the same fundamental group, and the same holonomy Lie algebra, yet different homotopy Lie algebras. 1. Definitions and statements of results 1.1. Holonomy and homotopy Lie algebras. Fix a field k of characteristic 0. Let A be a graded, graded-commutative...
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 ...