Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-24T13:23:39.212Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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