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Cohomology with exotic supports and the generalized excision

Part of: Homology and cohomology theories

Published online by Cambridge University Press:  09 April 2009

Satya Deo ,
Dalip Singh Jamwal  and
Ram Krishan
Satya Deo
Affiliation:
Department of Mathematics, University of JammuJammu-180 001, India
Dalip Singh Jamwal
Affiliation:
Department of Mathematics, University of JammuJammu-180 001, India
Ram Krishan
Affiliation:
Department of Mathematics, University of JammuJammu-180 001, India
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Abstract

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The main result proved in this paper is the following. Suppose X1, X2 are two subspaces of a space X such that X = Int(X1)∪ X2 = X1 ∪ Int(X2). Then the pair (X1, X2) is a ϕ on X. This result settles an open question and includes all known results on ϕ-excisiveness in sheaf cohomology as its special cases. We construct several several examples to illustrate our main theorem and to show that it is, in fact, quite sharp.

MSC classification

Secondary: 55N30: Sheaf cohomology 55N40: Axioms for homology theory and uniqueness theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 3 , December 1988 , pp. 326 - 340
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Bredon, G. E., Sheaf theory (McGraw-Hill, New York, 1967).Google Scholar
[2]Deo, S., ‘An example of nonexcisiveness in sheaf cohomology’, Proc. Amer. Math. Soc. 47 (1975), 501–503.CrossRefGoogle Scholar
[3]Deo, S., ‘One dimensional manifold is of cohomological dimension two’, Proc. Amer. Math. Soc. 52 (1975), 445–446.CrossRefGoogle Scholar
[4]Deo, S., ‘The cohomological dimension of an n-manifold is n + 1’, Pacific J. Math. 67 (1976), 154–160.CrossRefGoogle Scholar
[5]Godement, R., Topologie algébrique et théorie des faisceaux (Hermann, Paris, 1958).Google Scholar
[6]Spanier, E. H., Algebraic topology (McGraw-Hill, New York, 1966).Google Scholar