Cobordisme des surfaces plongées dans S4

Vincent Blanlœil, Osamu Saeki

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We show that a closed connected surface embedded in S4 = ∂B5 bounds a handlebody of dimension 3 embedded in B5 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 S5. We also give a new proof of Rohlin's theorem on embeddings of 3-manifolds into R5.

Original languageFrench
Pages (from-to)751-765
Number of pages15
JournalOsaka Journal of Mathematics
Issue number4
Publication statusPublished - Dec 1 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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