Linking of 2-spheres in 4-space

The notion of link homotopy, or “linking modulo knotting”, was introduced by Milnor for classical links in 1954, when he showed that his non-repeating mu-invariants give the complete obstruction to a link being link-homotopically trivial. 

 

In the setting of link homotopy for 2-spheres in 4-space fundamental differences from the classical setting quickly appear, and this talk will describe results and open questions, from the first nontrivial examples to the 2-component classification and new 3-component phenomena.