Links which are unknottable by maps

Howard Wilson Lambert

Vol. 65 (1976), No. 1, 109–112

DOI: 10.2140/pjm.1976.65.109

Abstract

Let L be a piecewise linear (PL) link of two components in the Euclidean 3-sphere S³ (i.e., L = L₁ ∪L₂ where L₁, L₂ are disjoint polygonal simple closed curves in S³. In Theorem 1 of this paper we give a geometric condition on L which implies it is unknottable. In Theorem 2, we show that there is an infinite class of links of two components which are unknottable.

Mathematical Subject Classification

Primary: 57A10, 57A10

Secondary: 55A25

Milestones

Received: 8 October 1975

Revised: 26 April 1976

Published: 1 July 1976