P-19 Higher Order Linking Up to Shake Concordance

Buller Hall

A link is an embedding of some number of circles into three dimensional space that may be knotted or linked together. They have been well-studied for their deep connections to the study of 3- and 4-manifolds as well as their applications to many fields, including the linking that occurs in DNA. Here, we explore a number of equivalence relations on the set of links--isotopy, concordance, and shake concordance--and show how Milnor's mu invariants, a measure of higher order linking, are at least partially preserved under each of these equivalences. This work calls for further study to see what other properties of links are preserved under shake concordance.