Some aspherical manifolds
type: Item
instance of: scholarly article
title: Some aspherical manifolds
zbMATH Open document ID: 0631.57019
DOI: 10.1215/S0012-7094-87-05507-4
author: Michael W. Davis
published in: Duke Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: Let Y be the space of real, tridiagonal, symmetric, \((n+1)\times (n+1)\) matrices. Let A be any set of \((n+1)\) distinct real numbers, and let P denote the set of matrices in Y with spectrum equal to A. The manifold P has been shown by Carlos Tomei to be a closed aspherical n-dimensional manifold. This paper provides two different generalizations of the manifold P. The first generalization is based upon actions of Coxeter groups, with P arising in the special case of the symmetric group. The second construction is based on real semisimple split Lie algebras, and P occurs for \(s\ell (n+1,R)\).
Mathematics Subject Classification ID: 57R15
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 4026364
zbMATH Keywords: space of real, tridiagonal, symmetric, \((n+1)\times (n+1)\) matrices
zbMATH Keywords: closed aspherical n-dimensional manifold
zbMATH Keywords: actions of Coxeter groups
zbMATH Keywords: real semisimple split Lie algebras
MaRDI profile type: Publication
cites work: Q5580319
cites work: Groups generated by reflections and aspherical manifolds not covered by Euclidean space
cites work: The homology of a space on which a reflection group acts
cites work: The Cohomology of an Isospectral Flow
cites work: Q3942064
cites work: The solution to a generalized Toda lattice and representation theory
cites work: Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
cites work: A decomposition of the group algebra of a finite Coxeter group
cites work: Characteristic numbers of 3-manifolds
cites work: The topology of isospectral manifolds of tridiagonal matrices
full work available at URL: s0012-7094-87-05507-4
OpenAlex ID: W1983276153
description: scientific article; zbMATH DE number 4026364