Description
Springer An Invitation to Alexandrov Geometry CAT(0) Spaces 2019 Edition by Stephanie Alexander, Vitali Kapovitch, Anton Petrunin
Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard-Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds. Table of contents : - 1 Preliminaries.- 2 Gluing theorem and billiards.- 3 Globalization and asphericity.- 4 Subsets.- 5 Semisolutions.