Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57N10, 57N70

Retrieve articles in all journals with MSC: 57N10, 57N70

Additional Information

Keywords: Surface, $ 3$-manifold, $ 4$-manifold, nonorientable, bordism, cobordism, Dehn surgery, Heegaard diagram
Article copyright: © Copyright 1992 American Mathematical Society