The disjoint curve property

Schleimer, Saul¹

¹ Department of Mathematics, University of Illinois at Chicago, 851 South Morgan Street, Chicago, Illinois 60607, USA

Geometry & topology, Tome 8 (2004) no. 1, pp. 77-113.

Résumé

A Heegaard splitting of a closed, orientable three-manifold satisfies the disjoint curve property if the splitting surface contains an essential simple closed curve and each handlebody contains an essential disk disjoint from this curve. A splitting is full if it does not have the disjoint curve property. This paper shows that in a closed, orientable three-manifold all splittings of sufficiently large genus have the disjoint curve property. From this and a solution to the generalized Waldhausen conjecture it would follow that any closed, orientable three manifold contains only finitely many full splittings.

Détail

DOI : 10.2140/gt.2004.8.77

Keywords: Heegaard splittings, disjoint curve property, Waldhausen Conjecture

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