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. found the first example of a wild arc, and found another example called the Fox-Artin arc whose complement is not simply connected.
Two very similar wild arcs appear in the article. Example 1.1 is most generally referred to as the Fox-Artin wild arc. The crossings have the regular sequence over/over/under/over/under/under when following the curve from left to right.
The left end-point 0 of the closed unit interval
[0,1]
R3
S3
Example 1.1* has the crossing sequence over/under/over/under/over/under. According to, page 982: "This is just the chain stitch of knitting extended indefinitely in both directions."
This arc cannot be continuously deformed to produce Example 1.1 in
R3
S3
Also shown here is an alternative style of diagram for the arc in Example 1.1*.