Torsion in the space of commuting elements in a Lie group
Torsion in the space of commuting elements in a Lie group

Masahiro Takeda, Kyoto University
Online Talk
Zoom link: https://princeton.zoom.us/j/92116764865
Passcode: 114700
Let $\mathrm{Hom}(\Z^m,G)$ denote the space of commuting $m$tuples in a Lie group $G$. This space is identified with the based moduli space of flat bundles over a torus, so it is an important object not only in topology but also in geometry and physics. I will talk about torsion in the homology of $\mathrm{Hom}(\Z^m,G)$. We prove that for $m\geq 2$, $\mathrm{Hom}(\Z^m,SU(n))$ has $p$torsion in homology if and only if $p\leq n$. The proof includes a new homotopy decomposition of $\mathrm{Hom}(\Z^m,G)$ in terms of a homotopy colimit.
This talk is based on the joint work with Daisuke Kishimoto.