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An Invitation to Alexandrov Geometry

CAT(0) Spaces

  • Book
  • © 2019


  • 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

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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About this book

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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Table of contents (4 chapters)


“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)

Authors and Affiliations

  • Department of Mathematics, University of Illinois, Urbana, USA

    Stephanie Alexander

  • Department of Mathematics, University of Toronto, Toronto, Canada

    Vitali Kapovitch

  • Department of Mathematics, Pennsylvania State University, University Park, USA

    Anton Petrunin

Bibliographic Information

  • Book Title: An Invitation to Alexandrov Geometry

  • Book Subtitle: CAT(0) Spaces

  • Authors: Stephanie Alexander, Vitali Kapovitch, Anton Petrunin

  • Series Title: SpringerBriefs in Mathematics

  • DOI:

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Author(s), under exclusive licence to Springer Nature Switzerland AG 2019

  • Softcover ISBN: 978-3-030-05311-6Published: 11 May 2019

  • eBook ISBN: 978-3-030-05312-3Published: 08 May 2019

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: XII, 88

  • Number of Illustrations: 91 b/w illustrations

  • Topics: Differential Geometry, Group Theory and Generalizations

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