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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An extension of Rourke's proof that $ \Omega\sb 3=0$ to nonorientable manifolds


Authors: Fredric D. Ancel and Craig R. Guilbault
Journal: Proc. Amer. Math. Soc. 115 (1992), 283-291
MSC: Primary 57N10; Secondary 57N70
MathSciNet review: 1092913
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Abstract: A classical result in manifold theory states that every closed $ 3$-manifold bounds a compact $ 4$-manifold. In 1985 C. Rourke discovered a strikingly short and elementary proof of the orientable case of this theorem $ ({\Omega _3} = 0)$. In this note we show that Rourke's approach can be extended to include nonorientable $ 3$-manifolds.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1092913-0
PII: S 0002-9939(1992)1092913-0
Keywords: Surface, $ 3$-manifold, $ 4$-manifold, nonorientable, bordism, cobordism, Dehn surgery, Heegaard diagram
Article copyright: © Copyright 1992 American Mathematical Society