Some aspherical manifolds (Q1094710)

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 \(s\ell (n+1,R)\).