Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-19T06:53:17.219Z Has data issue: false hasContentIssue false
  • English
  • Français

Calculations of cylindrical p-homotopy groups

Published online by Cambridge University Press:  20 January 2009

R. Ayala ,
E. Domínguez  and
A. Quintero
R. Ayala
Affiliation:
Departamento de Geometría Y TopologíaFacultad de matemáticasUniversidad de Sevilla41012 Sevilla, Spain
E. Domínguez
Affiliation:
Departamento de Geometría Y TopologíaFacultad de matemáticasUniversidad de Sevilla41012 Sevilla, Spain
A. Quintero
Affiliation:
Departamento de MatemáticasFacultad de CienciasUniversidad de Zaragoza50009 Zaragoza, Spain
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The definitions of the various proper homotopy groups correspond to three main geometrical ideas: sequences of spheres converging to a Freudenthal end (Brown groups); infinite cylinders giving the mobility of spheres towards a proper end (Čerin-Steenrod groups); sequences of spheres, each one movable to the next one following a proper end (Čech groups). The Brown and Čech groups have a rather complex structure and the calculations of these groups are very difficult (see [4]). The Čerin-Steenrod groups have a much simpler structure and this fact eases the computations.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 3 , October 1989 , pp. 401 - 413
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCES

1.Ayala, R., Domínguez, E., Quintero, A., Cylindrical p-homotopy groups, preprint.Google Scholar
2.Baues, H. J., Algebraic homotopy (Cambridge Studies in Advanced Mathematics, 15, 1987).Google Scholar
3.Brin, M. and Thickstun, T. L., On the proper Steenrod homotopy groups and proper embeddings of planes into 3 manifolds, Trans. Amer. Math. Soc. 289 (1985), 737–755.CrossRefGoogle Scholar
4.Brown, E. M., On the proper homotopy type (Lecture Notes Mathematics 375, Springer-Verlag, 1974).Google Scholar
5.ČErin, Z., On various relative proper homotopy groups, Tsukuba J. Math. 4 (1980) 177–202.Google Scholar
6.Domínguez, E., Hernández, L. J., Remarks about proper ends, preprint.Google Scholar
7.Domínguez, E., Hernández, L. J., Unas notas sobre los finales de un espacio, preprint.Google Scholar
8.Edwards, D. A., Hastings, H. M., Čech and Steenrod homotopy theories with applications to Geometric Topology (Lectures Notes Mathematics 542, Springer-Verlag, 1976).CrossRefGoogle Scholar
9.Jackson, J. R., On homotopy groups of function spaces, Amer. J. Math. 74 (1952), 241–252.CrossRefGoogle Scholar
10.Koh, S. S., Note on the homotopy properties of the components of the mapping space Xsp, Proc. Amer. Math. Soc. 11 (1960), 896–904.Google Scholar
11.Maunder, C. R. F., Algebraic Topology (Van Nostrand, 1970).Google Scholar
12.Porter, T., Čech and Steenrod homotopy and the Quigley exact couple in strong shape and proper homotopy theory, J. Pure Appl. Alg. 24 (1983), 303–312.CrossRefGoogle Scholar
13.Porter, T., Homotopy groups for strong shape and proper homotopy, Convegno di Topologia. Suppl. Rend. Circolo Mat. Palermo 4 (1984), 101–113.Google Scholar
14.Spanier, E., Algebraic Topology (McGraw-Hill, 1966).Google Scholar