Release Time:2019-03-09  Hits:

Indexed by: Journal Papers

Date of Publication: 2015-07-01

Journal: SCIENCE CHINA-MATHEMATICS

Included Journals: Scopus、SCIE

Volume: 58

Issue: 7

Page Number: 1499-1510

ISSN: 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.