Overview
- 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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Table of contents (4 chapters)
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Front Matter
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Back Matter
Keywords
- metric spaces
- Gromov–Hausdorff convergence
- Model angles and triangles.
- Space of directions and tangent space
- Geodesics
- Alexandrov geometry
- Gluing theorem and billiards
- Reshetnyak’s gluing theorem
- Reshetnyak’s puff pastry
- 4-point condition
- Polyhedral spaces
- Exotic aspherical manifolds
- ASPHERICITY
- Sets with smooth boundary
- Cubical complexes
- Two-convex hull
- Shefel’s theorem
- Riemannian geometry
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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Authors and Affiliations
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: https://doi.org/10.1007/978-3-030-05312-3
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