Knots and links made of one-dimensional lines embedded in a three-dimensional space are archetypes of topological intricacies.  Their classification involves the number of crossings which are, by definition, immune against the rewiring. Physical knots made of ropes or fishing lines are  in practice also immune against the rewiring of their crossings. 

Linear topological defects such as disclinations or dislocations can also be tied into knots and links but in this case the immunity against the rewiring of crossings is not always granted.  An exhaustive and accessible review on this topics was written