Glasnik Matematicki, Vol. 47, No. 1 (2012), 193-205.

ORBIT PROJECTIONS AND G-ANR-RESOLUTIONS

Alexander Bykov and Aura Lucina Kantún Montiel

Benemérita Universidad Autónoma de Puebla, Facultad de Ciencias Físico Matemáticas, Av. San Claudio y Rio Verde, Ciudad Universitaria, Colonia San Manuel, CP 72570, Puebla, Pue., México

Abstract.   We consider the orbit projection p_E:E → E/G of a G-space E with only one orbit type. We show that p_E admits a G-ANR-resolution consisting of G-fibrations if G is a compact metrizable group.

2010 Mathematics Subject Classification.   54C55, 54C56, 54H15.

Key words and phrases.   Fibration, orbit space, G-ANR.

DOI: 10.3336/gm.47.1.18

References:

1. S. A. Antonyan, Equivariant embeddings into G-AR's, Glas. Mat. Ser. III 22(42) (1987), 503-533.
   MathSciNet    

2. S. A. Antonyan, Retraction properties of an orbit space, Math. USSR-Sb. 65 (1990), 305-321.
   MathSciNet     CrossRef

3. S. A. Antonyan, The existence of a slice for an arbitrary compact transformation group, Mat. Zametki 56 (1994), 3-9 (in Russian); English transl.: Math. Notes 56 (1994), 1101-1104.
   MathSciNet     CrossRef

4. S. A. Antonyan, Extensorial properties of orbit spaces of proper group actions, Topology Appl. 98 (1999), 35-46.
   MathSciNet     CrossRef

5. S. A. Antonyan, Compact group actions on equivariant absolute neighborhood retracts and their orbit spaces, Topology Appl. 158 (2011), 141-151.
   MathSciNet     CrossRef

6. S. A. Antonyan and S. Mardešić, Equivariant shape, Fund. Math. 127 (1987), 213-224.
   MathSciNet    

7. A. Bykov, The homogeneous space G/H as an equivariant fibrant space, Topology Appl. 157 (2010), 2604-2612.
   MathSciNet     CrossRef

8. A. Bykov and M. Texis, Equivariant strong shape, Topology Appl. 154 (2007), 2026-2039.
   MathSciNet     CrossRef

9. G. E. Bredon, Introduction to compact transformation groups, Academic Press, New York, 1972.
   MathSciNet    

10. R. K. Lashof, Equivariant bundles, Illinois J. Math. 26 (1982), 257-271.
    MathSciNet    

11. S. Mardešić, Approximate polyhedra, resolutions of maps and shape fibrations, Fund. Math. 114 (1981), 53-78.
    MathSciNet    

12. R. S. Palais, The classification of G-spaces, Memoirs AMS 36, 1960.
    MathSciNet    

13. L. S. Pontrjagin, Topological groups, Princeton Univ. Press, 1939.
    MathSciNet    

14. T. tom Dieck, Transformation groups, Walter de Gruyter, Berlin-New York, 1987.
    MathSciNet     CrossRef