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论文类型：期刊论文

发表时间：2018-08-01

发表刊物：JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

收录刊物：SCIE

卷号：27

期号：9,SI

ISSN号：0218-2165

关键字：Curve complex; subsurface projection; keen Heegaard splitting; geodesic

摘要：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.