An Invitation to Alexandrov Geometry
CAT(0) Spaces
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Beschreibung
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.
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
Autor*in
Stephanie Alexander
Themen in »An Invitation to Alexandrov Geometry«
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
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“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)
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