Year: 2004
Type: article
Abstract: 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 [Thompson, 1999].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.
Source: Geometry & Topology
DOI: 10.2140/gt.2004.8.77
Author: Saul Schleimer
Institution: University of Illinois Chicago
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2149722159