This talk will discuss the notion of link homotopy, which was first defined by John Milnor in his seminal paper "Link Groups" in 1954, and has been steadily studied since then. Defined for classical links, it is often colloquially described as "linking modulo knotting", as it tries to capture the linking interactions between different components of a link while leaving out the knottedness of each individual component. Milnor himself defined the classical invariants for link homotopy, the link group and the "higher-order linking number" numerical invariants. Since then, many generalizations, new invariants and different viewpoints have been introduced. This talk will explore some of them, along with potential future results.
