紀要論文

紀要論文

text

2005-12

Osaka Journal of Mathematics. 2005, 42(4), p. 751-765

Cobordisme des surfaces plongees dans S⁴

Osaka University and Osaka City University, Departments of Mathematics

フランス語

text

2005-12

We show that a closed connected surface embedded in S^4 = ∂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 R^5.

10.18910/4229

4229

Cobordisme des surfaces plongees dans S⁴

Osaka University and Osaka City University, Departments of Mathematics

フランス語

2005-12

Osaka Journal of Mathematics

42

4

751

765

https://hdl.handle.net/11094/4229

10.18910/4229

https://doi.org/10.18910/4229