Determining incompressibility of surfaces in alternating knot and link complements

William W. Menasco

Vol. 117 (1985), No. 2, 353–370

DOI: 10.2140/pjm.1985.117.353

Abstract

In this paper we carry out the next necessary step in the study of closed incompressible surfaces in alternating link complements — determining when a given punctured surface in an alternating link complement is incompressible, pairwise incompressible and understanding when a “peripheral tubing” operation (which will produce a closed surface) preserves the incompressibility of a surface.

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57N10

Milestones

Received: 9 February 1983

Revised: 15 September 1983

Published: 1 April 1985