On the Second Homotopy Group of Spaces of Commuting Elements in Lie Groups
Offered By: IMSA via YouTube
Course Description
Overview
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.
Syllabus
José Manuel Gómez: On the second homotopy group of spaces of commuting elements in Lie groups
Taught by
IMSA
Related Courses
Introduction to Algebraic Topology (Part-I)Indian Institute of Technology Bombay via Swayam Introduction to Algebraic Topology (Part-II)
NPTEL via Swayam Intro to the Fundamental Group - Algebraic Topology with Tom Rocks Maths
Dr Trefor Bazett via YouTube Neural Sense Relations and Consciousness - A Diagrammatic Approach
Models of Consciousness Conferences via YouTube Classification of 2-Manifolds and Euler Characteristic - Differential Geometry
Insights into Mathematics via YouTube