Abstract
In this work we study the G-category of a G-manifold M by taking in consideration the fixed point set of a maximal torus of a compact Lie group G. The used method let us compute the G-category of sphere of every real irreducible, odd indexed representation Vl of the group G=SO(3). An application to a nonlinear Dirichlet problem, one of several possible, is given. Simplifying a proof of estimate of the G-category of the free part of a sphere we also show that the complement of saturation of fixed point set of a maximal torus is an open invariant subset of larger G-category than the free part of action and give particular computation for the spherical harmonics.
