L-S categories of simply-connected compact simple Lie groups of low rank

2002/02/13 by Norio Iwase, Mamoru Mimura · 1 citation
Mathematics · #math.AT #msc:55M30 #msc:55N20 #msc:22E20

paper · pdf

published as Categorical decomposition techniques in algebraic topology (Isle of Skye, 2001), 199--212, Progr. Math., 215, Birkhäuser, Basel, 2004 · 12 pages

arxiv created 2002/02/13 · arxiv updated 2009/11/30

Abstract

We determine the L-S category of Sp(3) by showing that the 5-fold reduced diagonal \widebarΔ₅ is given by ν², using a Toda bracket and a generalised cohomology theory h^* given by h^*(X,A) = \X/A,\mathbb S[0,2]\, where \mathbb S[0,2] is the 3-stage Postnikov piece of the sphere spectrum \mathbb S. This method also yields a general result that \cat(Sp(n)) ≥ n+2 for n ≥ 3, which improves the result of Singhof.

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