Geometry of Riemann Surfaces

doi:10.1017/CBO9781139194266

Riemann surfaces is a thriving area of mathematics with applications to hyperbolic geometry, complex analysis, fractal geometry, conformal dynamics, discrete groups, geometric group theory, algebraic curves and their moduli, various kinds of deformation theory, coding, thermodynamic formalism, and topology of three-dimensional manifolds. This collection of articles, authored by leading authorities in the field, comprises 16 expository essays presenting original research and expert surveys of important topics related to Riemann surfaces and their geometry. It complements the body of recorded research presented in the primary literature by broadening, re-working and extending it in a more focused and less formal framework, and provides a valuable commentary on contemporary work in the subject. An introductory section sets the scene and provides sufficient background to allow graduate students and research workers from other related areas access to the field.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-viii
- By Fred Gardiner
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Foreword
pp ix-xx
- By William Harvey, King's College London
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Semisimple actions of mapping class groups on CAT(0) spaces
pp 1-14
- By Martin R. Bridson, Mathematical Institute
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A survey of research inspired by Harvey's theorem on cyclic groups of automorphisms
pp 15-37
- By Emilio Bujalance, Departamento Matemáticas Fundamentales, F. J. Cirre, Departamento Matemáticas Fundamentales, UNED, G. Gromadzki, Institute of Mathematics, University of Gdańsk
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Algorithms for simple closed geodesics
pp 38-87
- By Peter Buser, Institut de Géométrie
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Matings in holomorphic dynamics
pp 88-119
- By Shaun Bullett, Queen Mary University of London
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Equisymmetric strata of the singular locus of the moduli space of Riemann surfaces of genus 4
pp 120-138
- By Antonio F. Costa, Departamento de Matemáticas Fundamentales, Milagros Izquierdo
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Diffeomorphisms and automorphisms of compact hyperbolic 2-orbifolds
pp 139-155
- By Clifford J. Earle, Cornell University
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Holomorphic motions and related topics
pp 156-193
- By Frederick P. Gardiner, Brooklyn College, Yunping Jiang, Queens College, Zhe Wang, CUNY Graduate Center
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Cutting sequences and palindromes
pp 194-216
- By Jane Gilman, Rutgers University, Linda Keen
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On a Schottky problem for the singular locus of A5
pp 217-237
- By Víctor González-Aguilera, Universidad Técnica Federico Santa María
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Non-special divisors supported on the branch set of a p-gonal Riemann surface
pp 238-259
- By Gabino González-Diez, Universidad Autónoma de Madrid
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A note on the lifting of automorphisms
pp 260-267
- By Rubén A. Hidalgo, Universidad Técnica Federico Santa María, Bernard Maskit, Stony Brook University
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Simple closed geodesics of equal length on a torus
pp 268-282
- By Greg McShane, Université de Grenoble I, Hugo Parlier
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On extensions of holomorphic motions—a survey
pp 283-308
- By Sudeb Mitra, Queens College of the City University of New York
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Complex hyperbolic quasi-Fuchsian groups
pp 309-355
- By John R. Parker, Ioannis D. Platis, University of Crete
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Geometry of optimal trajectories
pp 356-375
- By Mauro Pontani, University of Rome, Paolo Teofilatto
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Actions of fractional Dehn twists on moduli spaces
pp 376-395
- By Robert Silhol, Université Montpellier II
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Geometry of Riemann Surfaces

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Foreword
pp ix-xx

Semisimple actions of mapping class groups on CAT(0) spaces
pp 1-14

A survey of research inspired by Harvey's theorem on cyclic groups of automorphisms
pp 15-37

Algorithms for simple closed geodesics
pp 38-87

Matings in holomorphic dynamics
pp 88-119

Equisymmetric strata of the singular locus of the moduli space of Riemann surfaces of genus 4
pp 120-138

Diffeomorphisms and automorphisms of compact hyperbolic 2-orbifolds
pp 139-155

Holomorphic motions and related topics
pp 156-193

Cutting sequences and palindromes
pp 194-216

On a Schottky problem for the singular locus of A5
pp 217-237

Non-special divisors supported on the branch set of a p-gonal Riemann surface
pp 238-259

A note on the lifting of automorphisms
pp 260-267

Simple closed geodesics of equal length on a torus
pp 268-282

On extensions of holomorphic motions—a survey
pp 283-308

Complex hyperbolic quasi-Fuchsian groups
pp 309-355

Geometry of optimal trajectories
pp 356-375

Actions of fractional Dehn twists on moduli spaces
pp 376-395

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Geometry of Riemann Surfaces

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