Smooth and PL-Rigidity Problems on Locally Symmetric Spaces

Abstract

This is a survey on known results and open problems about Smooth and PL-Rigidity Problem for negatively curved locally symmetric spaces. We also review some developments about studying the basic topological properties of the space of negatively curved Riemannian metrics and the Teichmuller space of negatively curved metrics on a manifold.

arXiv commentarXiv admin note: substantial text overlap with arXiv:math/0206291, arXiv:math/0406132, arXiv:math/0607367 by other authors