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An Invitation to Alexandrov Geometry: CAT(0) Spaces: SpringerBriefs in Mathematics

Autor Stephanie Alexander, Vitali Kapovitch, Anton Petrunin
en Limba Engleză Paperback – 11 mai 2019
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.
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Specificații

ISBN-13: 9783030053116
ISBN-10: 3030053113
Pagini: 99
Ilustrații: XII, 88 p. 91 illus.
Dimensiuni: 155 x 235 mm
Greutate: 0.45 kg
Ediția:1st ed. 2019
Editura: Springer International Publishing
Colecția Springer
Seria SpringerBriefs in Mathematics

Locul publicării:Cham, Switzerland

Cuprins

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

Recenzii

“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)

Caracteristici

Explains the importance of CAT(0) geometry in geometric group theory Demonstrates Alexandrov geometry through applications and theorems Discusses Reshetnyak gluing theorem and Hadamard-Cartan globilization theorem