Thin position of a pair (3-manifold, 1-submanifold)

Chuichiro Hayashi and Koya Shimokawa

Vol. 197 (2001), No. 2, 301–324

DOI: 10.2140/pjm.2001.197.301

Abstract

We introduce the notions of Heegaard splittings and thin multiple Heegaard splittings of 1-submanifolds in compact orientable 3-manifolds, which are generalizations of those of bridge decompositions and thin positions. We show that either a thin multiple Heegaard splitting of 1-submanifold T is also a Heegaard splitting with minimal complexity or the exterior of T contains an essential surface with meridional boundary other than the boundary parallel annulus.

Milestones

Received: 15 February 1999

Published: 1 February 2001