Wild arc

In geometric topology, a wild arc is an embedding of the unit interval into 3-dimensional space not equivalent to the usual one in the sense that there does not exist an ambient isotopy taking the arc to a straight line segment.

Fox & Artin (1948) found another example, called the Fox-Artin arc, whose complement is not simply connected.

Two very similar wild arcs appear in the Fox & Artin (1948) article.

Example 1.1 (page 981) is most generally referred to as the Fox-Artin wild arc.

According to Fox & Artin (1948), page 982: "This is just the chain stitch of knitting extended indefinitely in both directions."

Fox-Artin arc Example 1.1
Fox-Artin arc Example 1.1*
The Fox–Artin wild arc (Example 1.1*) lying in drawn as a knot diagram . Note that each "tail" of the arc is converging to a point.