Algebraic Topology: Framed braids and homotopy groups of three-sphere

Speaker: Vasilii Ionin (St. Petersburg University)

Time: 2025-11-07 11:00-12:00
Location: 1410, SIMIS

Abstract: We discuss some fundamental connections between low-dimensional topology and homotopy theory. We give a new simple geometric proof of Rimvydas Krasauskas’ theorem computing the homotopy type of the simplicial group of framed surface braids. This suggests a simplicial model for the Lie group SU(2). Using this, we derive a well-known connection between Brunnian braids and homotopy groups of the 3-sphere, as explored by Fred Cohen, Jie Wu, and others.