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December 2005 Cobordisme des surfaces plongées dans $S^4$
Vincent Blanlœeil, Osamu Saeki
Osaka J. Math. 42(4): 751-765 (December 2005).


We show that a closed connected surface embedded in $S^{4} = \partial B^{5}$ bounds a handlebody of dimension 3 embedded in $B^{5}$ if and only if the Euler number of its normal bundle vanishes. Using this characterization, we show that two closed connected surfaces embedded in $S^{4}$ are cobordant if and only if they are abstractly diffeomorphic to each other and the Euler numbers of their normal bundles coincide. As an application, we show that a given Heegaard decomposition of a 3-manifold can be realized in $S^{5}$. We also give a new proof of Rohlin's theorem on embeddings of 3-manifolds into $\mathbf{R}^{5}$.


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Vincent Blanlœeil. Osamu Saeki. "Cobordisme des surfaces plongées dans $S^4$." Osaka J. Math. 42 (4) 751 - 765, December 2005.


Published: December 2005
First available in Project Euclid: 21 July 2006

MathSciNet: MR2195992

Rights: Copyright © 2005 Osaka University and Osaka City University, Departments of Mathematics


Vol.42 • No. 4 • December 2005
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