Neon bulbs and the unknotting of arcs in manifolds. (English) Zbl 0886.57003

Hass, Joel; Thompson, Abigail

J. Knot Theory Ramifications 6, No. 2, 235-242 (1997).

The light bulb trick states that all smooth arcs connecting two boundary components of \(S^2\times I\) are parallel. In this paper, the authors study several generalizations of the light bulb trick. They study properly embedded arcs in a 3-manifold \(M\) with connecting a point in a 2-sphere boundary component of \(M\) and a point in a distinct boundary component of \(M\), and show that in a variety of setting there is a unique isotopy class of arcs connecting two points.

Reviewer: Y.Akira (Tokyo)

MSC:

57M25

Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

light bulb trick; neon bulb trick; knotted arcs