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Indexed by:期刊论文

Date of Publication:2018-08-01

Journal:JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals:SCIE

Volume:27

Issue:9,SI

ISSN No.: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.