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On the second homotopy group of spaces of commuting elements in Lie groups

Ponente: Simon Gritschacher
Institución: University of Copenhagen
 Tipo de Evento: Investigación
Cuándo 18/02/2021
de 13:00 a 14:00
Dónde En linea (zoom)
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Resumen: In this talk we will consider the topological space of n-tuples of pairwise commuting elements in a Lie group G. This space arises as a moduli space of flat connections on principal G-bundles over the n-torus. We will describe homotopy and homology calculations. One of our main results is the description of the second homotopy group of the space of commuting pairs in any compact Lie group. The connection with gauge theory will be discussed. This is joint work with Alejandro Adem and José Manuel Gómez.