Normal Covering Spaces with Maximal Bottom of Spectrum

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 their general form, our results extend state art on under coverings.