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The relative Mayer–Vietoris sequence

Published online by Cambridge University Press:  24 October 2008

Richard Steiner
Richard Steiner
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
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Extract

The object of this paper is to generalize the relative Mayer-Vietoris sequence of Eilenberg and Steenrod([3], p. 42) by allowing both the containing spaces and the subspaces to vary. Fix a generalized homology theory h*. We call a couple of spaces {X1, X2} excisive (for h*) if they are subspaces of some larger space and the inclusion (X1, X1 ∩ X2) → (X1 ∪ X2, X2) induces an isomorphism under h* (see [4], pp. 208–9 for equivalent definitions).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 3 , May 1984 , pp. 423 - 425
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Adams, J. F.. Stable Homotopy and Generalised Homology. Chicago Lectures in Mathematics (University of Chicago Press, 1974).Google Scholar
[2]Eckmann, B. and Hilton, P. J.. Homotopy groups of maps and exact sequences. Comment. Math. Helv. 34 (1960), 271–304.CrossRefGoogle Scholar
[3]Eilenberg, S. and Steenrod, N.. Foundations of Algebraic Topology. Princeton Math. series 15 (Princeton University Press, 1952).Google Scholar
[4]Spanier, E. H.. Algebraic Topology (McGraw-Hill, 1966).Google Scholar
[5]Switzer, R. M.. Algebraic Topology – Homotopy and Homology. Grundlehren der math. Wissenschaften 212 (Springer-Verlag, 1975).CrossRefGoogle Scholar