Topology of the iso-spectral real manifolds associated with the generalized Toda lattices on semisimple Lie algebras

Details Topology of the iso-spectral real manifolds associated with the generalized Toda lattices on semisimple Lie algebras Topology of the iso-spectral real manifolds associated with the generalized Toda lattices on semisimple Lie algebras

2000-10-12

arxiv.org/abs/math/0010127v1

Mathematics

Geometric Topology

12 pages, AMSTeX, 3 figures, to appear in J.Phys.A Rport no:

Scientific paper

10.1088/0305-4470/34/11/326

This paper concerns the topology of isospectral real manifolds of certain Jacobi elements associated with real split semisimple Lie algebras. The manifolds are related to the compactified level sets of the generalized (nonperiodic) Toda lattice equations defined on the semisimple Lie algebras. We then give a cellular decomposition and the associated chain complex of the manifold by introducing colored Dynkin diagrams which parametrize the cells in the decomposition. We also discuss the Morse chain complex of the manifold.

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