Ohshika K. In the Tradition of Thurston II. Geometry and Groups 2022

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Ohshika K. In the Tradition of Thurston II. Geometry and Groups 2022

Textbook in PDF format The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. 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 topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups. Preface Introduction A Survey of Complex Hyperbolic Kleinian Groups Möbius Structures, Hyperbolic Ends and k-Surfaces in Hyperbolic Space Cone 3-Manifolds A Survey of the Thurston Norm From Hyperbolic Dehn Filling to Surgeries inRepresentation Varieties Acute Geodesic Triangulations of Manifolds Signature Calculation of the Area Hermitian Form on Some Spaces of Polygons Equilateral Convex Triangulations of R P2 with Three Conical Points of Equal Defect Combination Theorems in Groups, Geometry and Dynamics On the Pullback Relation on Curves Induced by a Thurston Map The Pullback Map on Teichmüller Space Induced from a Thurston Map A Classification of Postcritically Finite Newton Maps The Development of the Theory of Automatic Groups Geometry and Combinatorics via Right-Angled Artin Groups Index