Geometry and Topology of Geometric Limits I
In this chapter, we classify completely, up to isometry, hyperbolic 3-manifolds corresponding to geometric limits of Kleinian surface groups isomorphic to π1(S) for a finite-type hyperbolic surface S. In the first of the three main theorems which constitu
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e Tradition of Thurston Geometry and Topology
In the Tradition of Thurston
Ken’ichi Ohshika • Athanase Papadopoulos Editors
In the Tradition of Thurston Geometry and Topology
Editors Ken’ichi Ohshika Department of Mathematics Gakushuin University Tokyo, Japan
Athanase Papadopoulos Institut de Recherche Mathématique Avancée CNRS et Université de Strasbourg Strasbourg, France
ISBN 978-3-030-55927-4 ISBN 978-3-030-55928-1 (eBook) https://doi.org/10.1007/978-3-030-55928-1 Mathematics Subject Classification: 32G15, 30G60, 57M25, 57M50, 57M60, 57M07 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This is the first of a series of three volumes consisting of essays on Thurston’s contribution to mathematics, its development and its impact. The present volume contains 16 chapters. Some of them are surveys of Thurston’s works on several topics, including knot theory, geometrization of 3-manifolds, Kleinian groups, circle packings, the complex projective geometry of surfaces, and laminar groups. Other chapters are overviews of works that are directly inspired by Thurston’s ideas. They include topics such as the dynamical and counting problems for curves on hyperbolic surfaces, the study of surfaces of infinite type and their mapping class groups, the complex-analytic geometry of Teichmüller space, a stratification of moduli spaces of polynomials, and there are two chapters dedicated to the recent activity on anti-de Sitter geometry and quasi-Fuchsian co-Minkowski manifolds, two theories whose development follows closely Thurston’s ideas that he introduced in his study of hyperbolic geometry. All the chapters in this volume are self-contained and p
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