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

Published online by Cambridge University Press:  03 June 2010

ALEJANDRO ADEM ,
FREDERICK R. COHEN  and
JOSÉ MANUEL GÓMEZ
ALEJANDRO ADEM
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver BC V6T1Z2, Canada. e-mail: adem@math.ubc.ca
FREDERICK R. COHEN
Affiliation:
Department of Mathematics, University of Rochester, Rochester NY 14627, U.S.A. e-mail: cohf@math.rochester.edu
JOSÉ MANUEL GÓMEZ
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver BC V6T1Z2, Canada. e-mail: josmago@math.ubc.ca
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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(ℤn, U) and Rep(ℤn, Sp) are explicitly described as finite products of Eilenberg–MacLane spaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 3 , November 2010 , pp. 455 - 490
Copyright
Copyright © Cambridge Philosophical Society 2010

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