English

Stable splittings, spaces of representations and almost commuting elements in Lie groups

Algebraic Topology 2015-05-20 v1 Group Theory

Abstract

In this paper the space of almost commuting elements in a Lie group is studied through a homotopical point of view. In particular a stable splitting after one suspension is derived for these spaces and their quotients under conjugation. A complete description for the stable factors appearing in this splitting is provided for compact connected Lie groups of rank one.By using symmetric products, the colimits \Rep(Zn,SU)\Rep(\Z^n, SU), \Rep(Zn,U)\Rep(\Z^n,U) and \Rep(Zn,Sp)\Rep(\Z^n, Sp) are explicitly described as finite products of Eilenberg-MacLane spaces.

Keywords

Cite

@article{arxiv.1010.0735,
  title  = {Stable splittings, spaces of representations and almost commuting elements in Lie groups},
  author = {Alejandro Adem and Frederick R. Cohen and Jose Manuel Gomez},
  journal= {arXiv preprint arXiv:1010.0735},
  year   = {2015}
}

Comments

37 Pages. To appear in Math. Proc. Camb. Phil. Soc

R2 v1 2026-06-21T16:23:42.778Z