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Proper pointed maps from ℝn+1 to a σ-compact space

Published online by Cambridge University Press:  24 October 2008

Luis J. Hernandez  and
Timothy Porter
Luis J. Hernandez
Affiliation:
Department of Geometry and Topology, Facultad de Ciencias, 50009 Zaragosa, Spain
Timothy Porter
Affiliation:
Department of Pure Mathematics, University College of North Wales, Bangor, Wales
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Abstract

In this paper we study the group of pointed proper homotopy classes of proper pointed maps from (ℝn+1, 0) to a pointed σ-compact space (X, x) and prove the existence of a diagram of exact sequences linking the groups with the Brown—Grossman groups , the Steenrod groups πn(X) and the classical Hurewicz homotopy groups πn(X).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 3 , May 1988 , pp. 457 - 462
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Brin, M. G. and Thickstun, T. L.. On proper Steenrod homotopy groups and proper embeddings of planes into 3-manifolds. Trans. Amer. Math. Soc. 289 (1985), 737–755.CrossRefGoogle Scholar
[2]Brown, E. M.. On the proper homotopy type of simplicial complexes. In Topology Conference, Lecture Notes in Math. vol. 375 (Springer-Verlag, 1975).CrossRefGoogle Scholar
[3]Brown, R.. Some non-abelian methods in homotopy theory and homological algebra. In Categorical Topology (Heldermann Verlag, 1984), pp. 108–146.Google Scholar
[4]Cordier, J.-M. and Porter, T.. Vogt's theorem on categories of homotopy coherent diagrams. Math. Proc. Cambridge Philos. Soc. 100 (1986), 65–90.CrossRefGoogle Scholar
[5]Cordier, J.-M. and Porter, T.. Homotopy limits and homotopy coherence. (Lectures given at Perugia, 1984.)Google Scholar
[6]Edwards, D. A. and Hastings, H. M.. Čech and Steenrod homotopy theories with applications to geometric topology. Lecture Notes in Math. vol. 542 (Springer-Verlag, 1976).CrossRefGoogle Scholar
[7]Grossman, J. W.. Homotopy groups of prospaces. Illinois J. Math. 20 (1976), 612–625.CrossRefGoogle Scholar
[8]Hernandez, L. J., Rivas Rodriguez, M. T. and Extremiana Aldana, J. I.. Unas notas sobre las equivalencias de homotopia propria. Preprint.Google Scholar
[9]Hernandez, L. J.. A note on proper homology and homotopy groups. Preprint.Google Scholar
[10]Porter, T.. Coherent prohomotopy theory. Cahiers Topologie Geom. Differentielle Catégoriques 19 (1978), 3–46.Google Scholar
[11]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
[12]Porter, T.. Homotopy groups for strong shape and proper homotopy. Rend. Circ. Mat. Palermo (2) 4 (1984), 101–113.Google Scholar
[13]Porter, T.. Proper homotopy, prohomotopy and coherence. Publ. Sem. Mat. García de Galdeano, Ser. II 10 (1987).Google Scholar
[14]Porter, T.. On the two definitions of Ho (proC). Topology Appl., to appear.Google Scholar
[15]Quigley, J. B.. An exact sequence from the nth to the (n–1)st fundamental groups. Fund. Math. 77 (1973), 195–210.CrossRefGoogle Scholar