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

Homotopy type of the nilpotent orbits in classical Lie algebras