Some aspherical manifolds

DOI10.1215/S0012-7094-87-05507-4zbMath0631.57019OpenAlexW1983276153MaRDI QIDQ1094710

Michael W. Davis

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1215/s0012-7094-87-05507-4

zbMATH Keywords

actions of Coxeter groupsclosed aspherical n-dimensional manifoldreal semisimple split Lie algebrasspace of real, tridiagonal, symmetric, \((n+1)\times (n+1)\) matrices

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15)

Related Items (27)

Weighted \(L^2\)-cohomology of Coxeter groups based on barycentric subdivisons ⋮ \(\ell^2\)-homology of right-angled Coxeter groups based on barycentric subdivisions ⋮ The Cohomology of an Isospectral Flow ⋮ Aspherical manifolds, relative hyperbolicity, simplicial volume and assembly maps. ⋮ 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 ⋮ Neighborly cubical spheres and a cubical lower bound conjecture ⋮ Lie algebraic aspects of the finite nonperiodic Toda flows ⋮ On the \(KO\)-groups of toric manifolds ⋮ \(m\)-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices ⋮ Right-angularity, flag complexes, asphericity ⋮ Reflection groups on Riemannian manifolds ⋮ Completely integrable gradient flows ⋮ Large values of cusp forms on \(\mathrm{GL}_n\) ⋮ The lower algebraic \(K\)-theory of \(\Gamma_{3}\) ⋮ Toda Flows and Isospectral Manifolds ⋮ Gromov positive scalar curvature conjecture and rationally inessential macroscopically large manifolds ⋮ Rigidity of Coxeter groups ⋮ 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 ⋮ Examples of buildings constructed via covering spaces ⋮ A convexity theorem for isospectral manifolds of Jacobi matrices in a compact Lie algebra ⋮ Asymptotic Hamiltonian dynamics: The Toda lattice, the three-wave interaction and the non-holonomic Chaplygin sleigh ⋮ Hamiltonian and gradient structures in the Toda flows ⋮ The signature of a toric variety. ⋮ Convex polytopes, Coxeter orbifolds and torus actions

Cites Work

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• The homology of a space on which a reflection group acts
• The topology of isospectral manifolds of tridiagonal matrices
• Groups generated by reflections and aspherical manifolds not covered by Euclidean space
• The solution to a generalized Toda lattice and representation theory
• Characteristic numbers of 3-manifolds
• A decomposition of the group algebra of a finite Coxeter group
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
• The Cohomology of an Isospectral Flow

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