Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-08-01

Journal: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals: SCIE

Volume: 27

Issue: 9,SI

ISSN: 0218-2165

Key Words: Curve complex; subsurface projection; keen Heegaard splitting; geodesic

Abstract: Suppose V-1 boolean OR(S) V-2 is a Heegaard splitting and D-i is an essential separating disk in Vi such that a component of V-i - D-i is homeomorphic to F-i x I, i = 1, 2. In this paper, we prove that if there is a locally complicated simplicial path in C(S) connecting partial derivative D-1 to partial derivative D-2, then the geodesic connecting partial derivative D-1 to partial derivative D-2 is unique. Moreover, we give a sufficient condition such that V-1 boolean OR(S) V-2 is keen and the geodesic between any pair of essential disks on the opposite sides has local uniqueness property.