Topological Components of Commuting Elements of Nilpotent Lie Groups

Explore the topological components of commuting elements in nilpotent Lie groups through this 51-minute lecture by Bernardo Villarreal from CIMAT Merida. Delve into the limitations of Pettet and Souto's work on deformation retracts in reductive connected Lie groups, and examine Goldman's counterexample using the reduced Heisenberg group. Investigate why the deformation retraction fails for n-by-n reduced upper unitriangular matrix groups with real entries. Learn about the proposed alternative approach of considering commuting elements of maximal nilpotent Lie groups of class 2, focusing on reduced generalized Heisenberg groups G_n. Discover the elegant description of components in Hom(Z^k,G_n), including their relationship to real symplectic Stiefel manifolds and parametrization by cohomology classes H^2(Z^k,Z) for large n. Gain insights into this joint work with O. Antolín-Camarena, expanding your understanding of topological components in nilpotent Lie groups.