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Bordism and Cobordism

Published online by Cambridge University Press:  24 October 2008

M. F. Atiyah
M. F. Atiyah
Affiliation:
Pembroke College, Cambridge
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Extract

In (10), (11) Wall determined the structure of the cobordism ring introduced by Thom in (9). Among Wall's results is a certain exact sequence relating the oriented and unoriented cobordism groups. There is also another exact sequence, due to Rohlin(5), (6) and Dold(3) which is closely connected with that of Wall. These exact sequences are established by ad hoc methods. The purpose of this paper is to show that both these sequences are ‘cohomology-type’ exact sequences arising in the well-known way from mappings into a universal space. The appropriate ‘cohomology’ theory is constructed by taking as universal space the Thom complex MSO(n), for n large. This gives rise to (oriented) cobordism groups MSO*(X) of a space X.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 2 , April 1961 , pp. 200 - 208
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

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