Classification of \(G\)-spaces. (English. Russian original) Zbl 0812.57024

Ageev, S. M.

Russ. Acad. Sci., Izv., Math. 41, No. 3, 581-591 (1993); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 56, No. 6, 1345-1357 (1992).

A complete solution is given of a problem due to R. S. Palais [The classification of \(G\)-spaces, Mem. Am. Math. Soc. 36 (1960; Zbl 0119.384)]. Namely, it is proved that for every compact group \(G\), the equivariant Hilbert cube is an \(n\)-universal \(G\)-space, for every \(n\).

Reviewer: D.Repovš (Ljubljana)

MSC:

57S10	Compact groups of homeomorphisms
57S15	Compact Lie groups of differentiable transformations
55R35	Classifying spaces of groups and \(H\)-spaces in algebraic topology
54C55	Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
54F45	Dimension theory in general topology
57N20	Topology of infinite-dimensional manifolds

Keywords:

compact Lie group; \(G\)-bundle; equivariant Hilbert cube; \(n\)-universal \(G\)-space

Citations:

Zbl 0119.384