Proof of Perelman's Stability Theorem


Vitali Kapovitch

University of Toronto

March 5, 2007


Abstract: We give a proof of the celebrated stability theorem of Perelman stating that for a  noncollapsing sequence of Alexandrov spaces  $X_i$ with curvature bounded below Gromov-Hausdorff converging to an Alexandrov space $X$,  $X_i$ is homeomorphic to $X$ for all large $i$.