Any closed orientable and smooth non-positively curved manifold M is known to admit a geometric characteristic splitting, analogous to the JSJ decomposition in three dimensions. We show that when this splitting consists of pieces which are Seifert fibered or pieces each of whose fundamental group has non-trivial centre, M collapses with bounded curvature and has zero Perelman invariant.

We prove that every non-positively curved locally symmetric manifold M of finite volume contains a compact set K such that no periodic maximal flat in M can be homotoped out of K. Este art́ıculo está dedicado a Cloe y a la madre que la parió.

We investigate a Gepner-like superstring model described by a combination of multiple minimal models and an N = 2 Liouville theory. This model is thought to be equivalent to the superstring theory on a singular noncompact Calabi-Yau manifold. We construct the modular invariant partition function of this model, and confirm the validity of an appropriate GSO projection. We also calculate the elli...

Abstract We study the property of spectral-tightness Riemannian manifolds, which means that bottom spectrum Laplacian separates universal covering space from any other normal a manifold. prove closed manifold is topological characterized by its fundamental group. As an application, we show non-positively curved, spectrally-tight if and only dimension Euclidean local de Rham factor zero. In thei...