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Indexed by:Journal Papers

Date of Publication:2015-07-01

Journal:SCIENCE CHINA-MATHEMATICS

Included Journals:SCIE、Scopus

Volume:58

Issue:7

Page Number:1499-1510

ISSN No.:1674-7283

Key Words:stabilization; Heegaard distance; subsurface projection

Abstract:A closed orientable Haken three manifold containing a non separating incompressible closed surface has two canonical Heegaard splittings, which are called self-amalgamation and bilateral self-amalgamation. Heegaard distance introduced by Hempel is a useful index in studying Heegaard splitting. This paper studies the stabilization problem for the bilateral self-amalgamation, and proves that if the distance of bilateral selfamalgamation of a Heegaard splitting is at least 9, then it is unstabilized, weakly reducible and irreducible.