An Invitation to Alexandrov Geometry: Cat(0) Spaces

ISBN-13: 9783030053116 / Angielski / Miękka / 2019 / 88 str.

Stephanie Alexander; Vitali Kapovitch; Anton Petrunin

Opis

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.

Recenzje

"This monograph is a brief and well crafted introduction into this highly active field. ... This book is a pleasure to read and is highly recommended as a concise and stimulating introduction to metric geometry." (M. Kunzinger, Monatshefte für Mathematik, Vol. 196 (1), 2021)

Spis treści

 1 Preliminaries.- 2 Gluing theorem and billiards.- 3 Globalization and asphericity.- 4 Subsets.- 5 Semisolutions.