Essential tangle decomposition from thin position of a link

Daniel J. Heath and Tsuyoshi Kobayashi

Vol. 179 (1997), No. 1, 101–117

DOI: 10.2140/pjm.1997.179.101

Abstract

In this paper, we develop the idea of Thompson which treats the relationship between bridge position, incompressible meridianal planar surfaces, and thin position. We show that for a link in thin position there exits a canonical depth 1 nested tangle decomposition with incompressible 2-spheres arising from the thin position (Proposition 3.7), and we show that there is a maximal essential tangle decomposition of the link that is closely related to the thin position (Theorem 4.3).

Milestones

Published: 1 May 1997