Naslov
Equivariant shape

Autori
Antonian, S. A. ; Mardešić, Sibe

Izvornik
Fundamenta mathematicae (0016-2736) 127 (1987), 3; 213-224

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
action of a compact topological group ; equivariant shape category ; resolutions and expansions of topological spaces ; G-resolutions ; G- expansions ; G-ANR-resolution

Sažetak
This paper deals with the construction of an equivariant shape category ShG for topological spaces endowed with an action of a (fixed) compact topological group G. The construction of ShG is an equivariant version of the inverse system approach to ordinary shape developed by the second author and J. Segal [Shape Theory (1982 ; Zbl 0495.55001)]. With obvious modifications, the definitions of resolutions and expansions of topological spaces can be applied to the equivariant case: This gives the concepts of G-resolutions and G- expansions of G-spaces. The basic theorems are the following. (1) Every G-space X admits a G-ANR-resolution, i.e. a G-resolution \b{;p};: X→X−− in pro-TopG (TopG = category of G-spaces and G-maps) such that \b{;X}; consists of G-ANRs. (2) For every G- resolution \b{;p};: X→X−−, the induced [\b{;p};]: X→[X−−] in pro-[TopG] ([TopG] = equivariant homotopy category of TopG) is a G-expansion. The category ShG is then defined as follows. The objects are all G-spaces ; the morphisms between G-spaces X, Y are equivalence classes of triples ([\b{;p};], [\b{;q};], [\b{;f};]), where [\b{;p};]: X→[X−−], [\b{;q};]: Y→[Y−−] are G-ANR-expansions and [\b{;f};]: [\b{;X};]→[Y−−] is a morphism of pro-[TopG]. A G-shape functor [TopG]→ShG can be defined in the obvious way.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA