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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Mirzakhani’s Curve Counting and Geodesic Currents
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Mirzakhani’s Curve Counting and Geodesic Currents
Viveka Erlandsson, Juan Souto (Gebundene Ausgabe, Englisch)
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Beschreibung
This monograph presents an approachable proof of Mirzakhani’s curve counting theorem, both for simple and non-simple curves. Designed to welcome readers to the area, the presentation builds intuition with elementary examples before progressing to rigorous proofs. This approach illuminates new and established results alike, and produces versatile tools for studying the geometry of hyperbolic… surfaces, Teichmüller theory, and mapping class groups. Beginning with the preliminaries of curves and arcs on surfaces, the authors go on to present the theory of geodesic currents in detail. Highlights include a treatment of cusped surfaces and surfaces with boundary, along with a comprehensive discussion of the action of the mapping class group on the space of geodesic currents. A user-friendly account of train tracks follows, providing the foundation for radallas , an immersed variation. From here, the authors apply these tools to great effect, offering simplified proofs of existing results and a new, more general proof of Mirzakhani’s curve counting theorem. Further applications include counting square-tiled surfaces and mapping class group orbits, and investigating random geometric structures. Mirzakhani’s Curve Counting and Geodesic Currents introduces readers to powerful counting techniques for the study of surfaces. Ideal for graduate students and researchers new to the area, the pedagogical approach, conversational style, and illuminating illustrations bring this exciting field to life. Exercises offer opportunities to engage with the material throughout. Basic familiarity with 2-dimensional topology and hyperbolic geometry, measured laminations, and the mapping class group is assumed. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
21.09.2022
Sprache
Englisch
EAN
9783031087042
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Progress in Mathematics
Sonderedition
Nein
Autor
Viveka Erlandsson, Juan Souto
Seitenanzahl
226
Einbandart
Gebundene Ausgabe
Illustriert von
Hugo Parlier
Schlagwörter
Mirzakhani curve counting, Counting closed geodesics, Mirzakhani curve counting for non-simple curves, Geodesic currents, Geodesic currents of cusped surfaces, Mapping class group, Teichmüller space, Train tracks hyperbolic surfaces, Immersed train track, Thurston measure, Square-tiled surfaces, Geometric structures on surfaces, Dynamics induced by group actions, Statistics of simple curves, Random pants decomposition
Thema-Inhalt
PBP - Topologie
GPFC - Kybernetik und Systemtheorie
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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