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

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

2002-02-13

arxiv.org/abs/math/0202122v1

Categorical decomposition techniques in algebraic topology (Isle of Skye, 2001), 199--212, Progr. Math., 215, Birkh\"auser, Ba

Mathematics

Algebraic Topology

12 pages

Scientific paper

We determine the L-S category of Sp(3) by showing that the 5-fold reduced diagonal $\widebar{\Delta}_5$ is given by $\nu^2$, 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 $\cat(Sp(n)) \geq n+2$ for $n \geq 3$, which improves the result of Singhof.

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