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

作者：Adem Alejandro^*; Cohen Frederick R; Gomez Jose Manuel

来源：Mathematical Proceedings of the Cambridge Philosophical Society, 2010, 149: 455-490.

DOI：10.1017/S0305004110000277

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(Z(n), SU), Rep(Z(n), U) and Rep(Z(n), Sp) are explicitly described as finite products of Eilenberg-MacLane spaces.

• 出版日期2010-11