Trace map, Cayley transform and LS category of Lie groups

Details Trace map, Cayley transform and LS category of Lie groups Trace map, Cayley transform and LS category of Lie groups

2009-07-04

arxiv.org/abs/0907.0751v1

Mathematics

Algebraic Topology

14 pages

Scientific paper

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

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