An Invitation to Alexandrov Geometry - CAT(0) Spaces

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.

List of contents

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

Summary

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.

Additional text

“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)

Report

"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)

Product details

• Authors: Stephani Alexander, Stephanie Alexander, Vital Kapovitch, Vitali Kapovitch, A Petrunin, Anton Petrunin
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2019
• EAN: 9783030053116
• ISBN: 978-3-0-3005311-6
• No. of pages: 88
• Dimensions: 156 mm x 9 mm x 237 mm
• Weight: 166 g
• Illustrations: XII, 88 p. 91 illus.
• Series: SpringerBriefs in Mathematics; SpringerBriefs in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; C, Gruppen und Gruppentheorie, Group Theory, Mathematics and Statistics, Differential Geometry, Groups & group theory, Group Theory and Generalizations, Riemannian geometry, Two-convex hull, Reshetnyak’s gluing theorem, Polyhedral spaces, Exotic aspherical manifolds, ASPHERICITY, Cubical complexes, Reshetnyak’s puff pastry, Shefel’s theorem, Gluing theorem and billiards, Sets with smooth boundary