Young Seminar of the session "Algebraic topology, geometric and combinatorial group theory"
timetable:
Tue 17 Feb, 15:40 - 16:20, Aula Dini
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seminar: Spaces of commuting elements in Lie groups
speaker: Mentor Stafa (Tulane University)abstract: The spaces of ordered pairwise commuting n-tuples in compact and connected Lie groups, denoted Hom(Zk,G), have been at the center of much recent study. We will give a brief overview of the current state of the problem. We then introduce an infinite dimensional topological space denoted Comm(G), reminiscent of a Stiefel variety, that assembles the spaces Hom(Zk,G) into a single space. This construction admits stable decompositions which allow the study of the spaces Hom(Zk,G) individually, and the Hilbert-Poincare series is calculated using Molien's theorem. The cohomology of Comm(G) is given in terms of the tensor algebra generated by the reduced homology of the maximal torus. This is joint work with Fred Cohen.
timetable:
Tue 17 Feb, 15:40 - 16:20, Aula Dini
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