An Invitation to Alexandrov Geometry CAT(0) Spaces /

• Main Authors: Alexander, Stephanie (Author, http://id.loc.gov/vocabulary/relators/aut), Kapovitch, Vitali (http://id.loc.gov/vocabulary/relators/aut), Petrunin, Anton (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: SpringerBriefs in Mathematics,
• Subjects: Differential geometry.; Group theory.; Differential Geometry.; Group Theory and Generalizations.
• Physical Description: XII, 88 p. 91 illus. online resource.
• ISBN: 9783030053123
• ISSN: 2191-8198
• DOI: 10.1007/978-3-030-05312-3

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.