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Indexed by:Journal Papers

Date of Publication:2016-01-01

Journal:PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

Included Journals:SCIE

Volume:144

Issue:1

Page Number:423-434

ISSN No.:0002-9939

Abstract:Let M = V boolean OR(S) W be a Heegaard splitting of a 3-manifold M and let F be a component of partial derivative M lying in partial derivative-V. A simple closed curve J in F is said to be distance degenerating if the distance of M-J = V-J boolean OR(S) W is less than the distance of M = V boolean OR(S) W where M-J is the 3-manifold obtained by attaching a 2-handle to M along J. In this paper, we will prove that for a strongly irreducible Heegaard splitting M = V boolean OR(S) W, if V is simple or M = V boolean OR(S) W is locally complicated, then the diameter of the set of distance degenerating curves in F is bounded.