Wild arc

Fox-Artin arc Example 1.1

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.

Antoine (1920) found the first example of a wild arc. Fox & Artin (1948) found another example, called the Fox-Artin arc, whose complement is not simply connected.