Mirzakhani S Curve Counting And Geodesic Currents
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Mirzakhani S Curve Counting And Geodesic Currents
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Author : Viveka Erlandsson
language : en
Publisher: Springer Nature
Release Date : 2022-09-20
Mirzakhani S Curve Counting And Geodesic Currents written by Viveka Erlandsson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-20 with Mathematics categories.
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.
Mirzakhani S Curve Counting And Geodesic Currents
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Author : Viveka Erlandsson
language : en
Publisher:
Release Date : 2022
Mirzakhani S Curve Counting And Geodesic Currents written by Viveka Erlandsson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Curves categories.
In The Tradition Of Thurston Iii
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Author : Ken’ichi Ohshika
language : en
Publisher: Springer Nature
Release Date : 2024-03-19
In The Tradition Of Thurston Iii written by Ken’ichi Ohshika and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-19 with Mathematics categories.
William Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The purpose of the present volume and of the other volumes in the same series is to provide a collection of articles that allows the reader to learn the important aspects of Thurston’s heritage. The topics covered in this volume include Kleinian groups, holomorphic motions, earthquakes from the Anti-de Sitter point of view, the Thurston and Weil–Petersson metrics on Teichmüller space, 3-manifolds, geometric structures, dynamics on surfaces, homeomorphism groups of 2-manifolds and the theory of orbifolds.
In The Tradition Of Thurston
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Author : Ken’ichi Ohshika
language : en
Publisher: Springer Nature
Release Date : 2020-12-07
In The Tradition Of Thurston written by Ken’ichi Ohshika and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-07 with Mathematics categories.
This book consists of 16 surveys on Thurston's work and its later development. The authors are mathematicians who were strongly influenced by Thurston's publications and ideas. The subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle packings, complex projective structures, hyperbolic geometry, Kleinian groups, foliations, mapping class groups, Teichmüller theory, anti-de Sitter geometry, and co-Minkowski geometry. The book is addressed to researchers and students who want to learn about Thurston’s wide-ranging mathematical ideas and their impact. At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.