  In the paper "The Second cohomology of nilpotent orbits in classical Lie
algebras, Kyoto J. Math. 60 (2020), no. 2, 717-799" by I. Biswas, P. Chatterjee
and C. Maity homotopy types of nilpotent orbits are explicitly described in the
case of real simple classical Lie algebras for which any maximal compact
subgroup in the associated adjoint group is not semisimple. In this paper we
extend the above description of homotopy type of nilpotent orbits to the
remaining cases of real simple classical Lie algebras for which any maximal
compact subgroup in the associated adjoint group is semisimple.
