An Invitation to Alexandrov Geometry
Springer International Publishing (Verlag)
978-3-030-05311-6 (ISBN)
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.
1 Preliminaries.- 2 Gluing theorem and billiards.- 3 Globalization and asphericity.- 4 Subsets.- 5 Semisolutions.
"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)
“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)
| Erscheinungsdatum | 12.05.2019 |
|---|---|
| Reihe/Serie | SpringerBriefs in Mathematics |
| Zusatzinfo | XII, 88 p. 91 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 165 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | 4-point condition • Alexandrov geometry • ASPHERICITY • cubical complexes • Exotic aspherical manifolds • geodesics • Gluing theorem and billiards • Gromov-Hausdorff convergence • Gromov–Hausdorff convergence • Metric Spaces • Model angles and triangles. • Polyhedral spaces • Reshetnyak's gluing theorem • Reshetnyak’s gluing theorem • Reshetnyak's puff pastry • Reshetnyak’s puff pastry • Riemannian Geometry • Sets with smooth boundary • Shefel's theorem • Shefel’s theorem • Space of directions and tangent space • Two-convex hull |
| ISBN-10 | 3-030-05311-3 / 3030053113 |
| ISBN-13 | 978-3-030-05311-6 / 9783030053116 |
| Zustand | Neuware |
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