Self and partial gluing theorems for Alexandrov spaces with a lower curvature bound

Abstract

This paper is devoted to prove that if an Alexandrov space of curvature not less than $\kappa$ with a codimension one extremal subset which admits an isometric involution with respect to the induced length metric, then the metric space obtained by gluing the extremal subset along the isometry is an Alexandrov space of curvature not less than $\kappa$. This is a generalization of Perelman's doubling and Petrunin's gluing theorems.