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SCINDEMENTS DE HEEGAARD DES VARIÉTÉS DE SEIFERT ELLIPTIQUES ET EUCLIDIENNES

Published online by Cambridge University Press:  08 April 2017

M. BOILEAU  and
J.-P. OTAL
M. BOILEAU
Affiliation:
Laboratoire E. Picard, Université Paul Sabatier, UMR 5580, 118 route de Narbonne, 31062 Toulouse Cédex, France
J.-P. OTAL
Affiliation:
Laboratoire de Mathématiques, École Normale Supérieure de Lyon, UMR 0128, 46 allée d'Italie, 69364 Lyon Cédex, France
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Abstract

It is proved that there is, up to isotopy, a unique irreducible Heegaard splitting in an orientable, closed, connected Seifert 3-manifold with an orientable elliptical or euclidean orbifold basis. Using Hamilton's and Lawson's results, the topological uniqueness is obtained of closed orientable minimal surfaces of a given genus g [ges ] 2, embedded in a closed orientable Riemannian 3-manifold with strictly positive Ricci curvature.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 63 , Issue 2 , April 2001 , pp. 501 - 512
Copyright
The London Mathematical Society 2001

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