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Unitary bordism of circle actions

Published online by Cambridge University Press:  20 January 2009

Czes Kosniowski  and
Mahgoub Yahia
Czes Kosniowski
Affiliation:
School of Mathematics, The University, Newcastle upon Tyne, England
Mahgoub Yahia
Affiliation:
School of Mathematics, University of Khartoum, Khartoum, Sudan
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The purpose of this paper is to describe , the bordism module of unitary T-manifolds, where T denotes the circle group S1. We give both an algebraic and a geometric description. The algebraic result is

where I = (i(1), i(2),…i(2n)) runs through all finite ordered 2n-tuples (n≧0) of non-negative integers which satisfy the conditions (a) i(l) + i(2n)≠0 and (b) if i(2n)≠0 then i(2n)=≠. The isomorphism is also described geometrically and this leads to geometric generators of .

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 1 , February 1983 , pp. 97 - 105
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

REFERENCES

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4.Ossa, E., Fixpunktfreie S 1-Aktionen, Math. Ann. 186 (1970), 45–52.CrossRefGoogle Scholar