Glasnik Matematicki, Vol. 35, No.2 (2000), 191-210.

FIBERWISE RETRACTION AND SHAPE PROPERTIES OF THE ORBIT SPACE

Sergey A. Antonyan, Rolando Jimenez and Sylvia de Neymet

Departamento de Matematicas, Facultad de Ciencias, UNAM, Circuito Exterior, C.U., 04510 Mexico D.F., Mexico
e-mail: antonyan@servidor.unam.mx

Instituto de Matematicas, UNAM, Av. Universidad S/N, Col. Lomas de Chamilpa, 62210 Cuernavaca, Morelos, Mexico
e-mail: rolando@matcuer.unam.mx

Departamento de Matematicas, Facultad de Ciencias, UNAM, Circuito Exterior, C.U., 04510 Mexico D.F., Mexico
e-mail: christ@servidor.unam.mx


Abstract.   From the point of view of retracts and shape theory, the category G-TOPB of G-spaces over a G-space B, where G is a compact group, is investigated. In particular, we prove that if B has only one orbit type and E is a metric G-ANR over B, then the orbit space E/G is an ANR over B/G. As an application we construct a fiberwise G-orbit functor μ : G-SHB SHB/G on shape level.

1991 Mathematics Subject Classification.   54C55, 54C56, 54H15, 54B15.

Key words and phrases.   Equivariant rectract, equivariant fiberwise shape, orbit space, G-ANR, G-shape, G-resolution.


Full text (PDF) (free access)
Glasnik Matematicki Home Page