On the Second Homotopy Group of Spaces of Commuting Elements in Lie Groups

Explore the computation of the second homotopy group of spaces in the form Hom(Z^n, G), where G is a compact Lie group, in this one-hour lecture by José Manuel Gómez from Universidad Nacional de Colombia. Delve into the specific case where G is compact, simply connected, and simple, demonstrating that π₂(Hom(Z², G)) = Z and discussing the obtainment of geometric generators. Learn about this complex topic based on joint work with Alejandro Adem and Simon Gritschacher, gaining insights into the intricate relationships between Lie groups and homotopy theory.

José Manuel Gómez: On the second homotopy group of spaces of commuting elements in Lie groups