Физико-математический клуб при ПОМИ и СПбГУ

In this talk, we will discuss some natural and fundamental connections between braids and homotopy theory. After introducing simplicial groups and braids, several natural connections between braids and homotopy theory will be established by investigating the structures on braids. In particular, the general homotopy groups of 2-spheres are determined by the Brunnian braids over the sphere modulo the Brunnian braids over the disk. Moreover the group of Brunnian braids over general surfaces other than 2-sphere or projective plane can be fully determined as symmetric commutator subgroups.