The topology of isospectral manifolds of tridiagonal matrices

DOI10.1215/S0012-7094-84-05144-5zbMath0558.57006MaRDI QIDQ762807

Carlos Tomei

Publication date: 1984

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Euler characteristicuniversal covering spaceCW-decompositionToda vector fieldtridiagonal matrices with fixed spectrum

Mathematics Subject Classification ID

Related Items (39)

Weighted \(L^2\)-cohomology of Coxeter groups based on barycentric subdivisons ⋮ \(\ell^2\)-homology of right-angled Coxeter groups based on barycentric subdivisions ⋮ Some aspherical manifolds ⋮ Representations of sl(n,\({\mathbb{C}})\) and the Toda lattice ⋮ The Cohomology of an Isospectral Flow ⋮ The Toda flows preserving small cells of the flag variety \(G/B\) and Kazhdan's \(x_{0}\)-grading ⋮ Universal realisators for homology classes ⋮ The Atiyah conjecture and \(L^2\)-cohomology computations ⋮ A new formulation of the generalized Toda lattice equations and their fixed point analysis via the momentum map ⋮ Lie algebraic aspects of the finite nonperiodic Toda flows ⋮ On the \(KO\)-groups of toric manifolds ⋮ Space of isospectral periodic tridiagonal matrices ⋮ \(m\)-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices ⋮ Linearizing Toda and SVD flows on large phase spaces of matrices with real spectrum ⋮ Symmetric Toda, gradient flows, and tridiagonalization ⋮ Gradient flows, adjoint orbits, and the topology of totally nonnegative flag varieties ⋮ \(\mathfrak{so}(p,q)\) Toda systems ⋮ An atlas for tridiagonal isospectral manifolds ⋮ Completely integrable gradient flows ⋮ Large values of cusp forms on \(\mathrm{GL}_n\) ⋮ Qualitative behavior of non-Abelian Toda-like flows ⋮ Painlevé analysis and normal forms theory ⋮ The asymptotics of Wilkinson's shift: Loss of cubic convergence ⋮ A Hessenberg-Jacobi isospectral flow ⋮ The Level Manifold of a Generalized Toda Equation Hierarchy ⋮ Fifty years of the finite nonperiodic Toda lattice: a geometric and topological viewpoint ⋮ Integrable systems and the topology of isospectral manifolds ⋮ The manifold of isospectral symmetric tridiagonal matrices and realization of cycles by aspherical manifolds ⋮ Toda lattices with indefinite metric. II: Topology of the iso-spectral manifolds ⋮ The resolutions of the singular loci of the Toda lattice on the split and connected reductive Lie groups ⋮ The Atiyah-Hitchin bracket and the open Toda lattice. ⋮ A convexity theorem for isospectral manifolds of Jacobi matrices in a compact Lie algebra ⋮ Orbit spaces for torus actions on Hessenberg varieties ⋮ Toda flows with infinitely many variables ⋮ Asymptotic Hamiltonian dynamics: The Toda lattice, the three-wave interaction and the non-holonomic Chaplygin sleigh ⋮ Manifolds of isospectral arrow matrices ⋮ Hamiltonian and gradient structures in the Toda flows ⋮ Parameterization by polytopes of intersections of orbits by conjugation ⋮ Convex polytopes, Coxeter orbifolds and torus actions

Cites Work

• Groups generated by reflections and aspherical manifolds not covered by Euclidean space
• Ends of maps. III: Dimensions 4 and 5
• The spectrum of Jacobi matrices
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
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