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.
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