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This paper concerns the topology of isospectral real manifolds of certainJacobi elements associated with real split semisimple Lie algebras. Themanifolds are related to the compactified level sets of the generalized(nonperiodic) Toda lattice equations defined on the semisimple Lie algebras. Wethen give a cellular decomposition and the associated chain complex of themanifold by introducing colored Dynkin diagrams which parametrize the cells inthe decomposition. We also discuss the Morse chain complex of the manifold.Comment: 12 pages, AMSTeX, 3 figures, to appear in J.Phys.A Rport no

Topology of the isospectral real manifolds associated with the generalized Toda lattices on semisimple Lie algebras