A property of manifolds compactly equivalent to compact manifolds

Length equivalent hyperbolic manifolds

In the case when M is an orientable Riemannian manifold of negative curvature L (M) and L(M) are related to the eigenvalue spectrum of M; that is, the set E (M) of all eigenvalues of the Laplace–Beltrami operator acting on L2(M) counted with multiplicities. For example, in this setting it is known that E (M) determines L(M) (see [3]). In the case of closed hyperbolic surfaces, the stronger stat...

Volumes of Compact Manifolds

We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or normalization of the manifold, that is, the generalization of the unit radius condition for spheres. For this aim we first describe the manifold with some pa...

Manifolds homotopy equivalent to Pn # Pn

We classify, up to homeomorphism, all closed manifolds having the homotopy type of a connected sum of two copies of real projective n-space. 1. Statement of results Let P = Pn(R) be real projective n-space. López de Medrano [LdM71] and C.T.C. Wall [Wal68, Wal99] classified, up to PL homeomorphism, all closed PL manifolds homotopy equivalent to P when n > 4. This was extended to the topological ...

Surgery on Compact Manifolds

Deformation Spaces Associated to Compact Hyperbolic Manifolds

Recently, there has been considerable interest in spaces of locally homogeneous (or geometric) structures on smooth manifolds, motivated by Thurston [6, 7]. If M is a smooth manifold, we will let C(M) denote the space of conformai structures (with marking) on M and P(M) the space of projective structures (with marking) on M. Since these spaces are a measure of the complexity of the fundamental ...