Release Time:2019-03-09  Hits:

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: 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.