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The aim of this paper is to use the so-called Cayley transform to compute theLS category of Lie groups and homogeneous spaces by giving explicit categoricalopen coverings. When applied to U(n), $U(2n)/Sp(n)$ and $U(n)/O(n)$ this methodis simpler than those formerly known. We also show that the Cayley transform isrelated to height functions in Lie groups, allowing to give a local linearmodel of the set of critical points. As an application we give an explicitcovering of $Sp(2)$ by categorical open sets. The obstacles to generalize theseresults to $Sp(n)$ are discussed.

Trace map, Cayley transform and LS category of Lie groups