Geometry, groups and dynamics : ICTS program : groups, geometry and dynamics, December 3-16, 2012, CEMS, Kumaun University, Almora, India / C.S. Aravinda [and five others], editors.

Format:

Book

Contributor:

Aravinda, C. S., 1963- editor.

Series:

Contemporary mathematics (American Mathematical Society) ; 639.

Contemporary Mathematics, 1098-3627 ; 639

Language:

English

Subjects (All):

Group theory.

Discrete groups.

Hyperbolic spaces.

Geometry, Non-Euclidean.

Physical Description:

1 online resource (371 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2015.

Language Note:

English

Summary:

This volume contains the proceedings of the ICTS Program: Groups, Geometry and Dynamics, held December 3-16, 2012, at CEMS, Almora, India. The activity was an academic tribute to Ravi S. Kulkarni on his turning seventy. Articles included in this volume, both introductory and advanced surveys, represent the broad area of geometry that encompasses a large portion of group theory (finite or otherwise) and dynamics in its proximity. These areas have been influenced by Kulkarni's ideas and are closely related to his work and contribution.

Contents:

Cover

Title page

Contents

Foreword

Preface

Complex Kleinian groups

Introduction

1. Kleinian groups in real hyperbolic space

2. Complex Kleinian groups

3. On the classification of projective automorphisms

4. Dynamics in complex dimension 2

5. Geometry in complex dimension 2

References

Complete Lorentzian 3-manifolds

1. Introduction

2. Basic Lorentzian geometry

3. Proper actions and locally homogeneous Lorentzian 3-manifolds

4. Affine deformations and the Margulis invariant

5. Einstein Universe

The Goldman bracket and the intersection of curves on surfaces

2. The \Z-module of curves

3. The Goldman bracket

4. Examples

5. Relation between the bracket of two curves and the number of intersection points.

6. Open problems and generalizations

An introduction to flows on homogeneous spaces

1. Homogeneous spaces

2. Measures on homogeneous spaces

3. Ergodic properties

4. Unitary representations

5. Flows on (2,\R)/Γ

6. Flows on ( ,\R)/Γ

7. Duality

8. Diophantine approximation

9. Geodesic flows and applications

Quantitative Geometry of Hyperbolic Manifolds

1. The Banach-Tarski paradox

2. Uniform restrictions on discrete groups

3. Quantitative Mostow rigidity

4. Diameter and homology

Discrete Groups and Riemann Surfaces

1. Prerequisites

2. Riemann surfaces

3. Holomorphic maps

4. Galois groups

5. Uniformization

6. Greenberg-Singerman extensions

7. Further reading

A Note on Chern's Theorem on Invariant Measures

2. Chern's Criterion for existence of Invariant measures

3. A New approach to Chern's Theorem

4. Cauchy-Crofton Type Formulae

Random Affine Lattices

References.

Upper central series for the group of unitriangular automorphisms of a free associative algebra

2. Some previous results and remark

3. Unitriangular group ₂

4. Unitriangular group ₃

5. Center of the unitriangular group _{ }, ≥4

Hermitian structure and bundles on /Γ

2. Hermitian structure on /Γ

3. Automorphisms of the pair ( ,Γ)

4. Homogeneous bundles on /Γ

5. Extendable homomorphisms from the lattice

Log-Riemann surfaces, Caratheodory convergence and Euler's formula

1.1. Acknowledgements

2. Log-Riemann surfaces

2.1. Definitions

2.2. Examples

3. Caratheodory Theorem for log-Riemann surfaces

3.1. Caratheodory convergence of log-Riemann surfaces

3.2. Convergence of uniformizations

Uniformization of simply connected finite type Log-Riemann surfaces

2. Cell decompositions of log-Riemann surfaces

2.1. Decomposition into stars

2.2. The skeleton and fundamental group

2.3. Truncation and approximation by finite sheeted surfaces

2.4. Compactness for uniformly finite type log-Riemann surfaces

2.5. Decomposition into Kobayashi-Nevanlinna cells

2.6. Kobayashi-Nevanlinna parabolicity criterion

3. Uniformization theorems

The Euler Characteristic of a Haken 4-Manifold

2. Basic Facts about Haken -Manifolds

3. Approach to the Sign Conjecture for Haken 4-Manifolds

4. Results

5. Determination of -function and the transformation law

6. Evaluation of the -function on Haken 4-cells

7. Concluding Discussion

Acknowledgements

A discreteness criterion for groups containing parabolic isometries

1. Preliminaries

2. The Criterion

3. The 4-dimensional case

On the -classes in a centrally finite division ring

2. Some Generalities on -Classes

3. -Classes in Centrally Finite Division Rings

4. Wedderburn's Theorem on Finite Division Rings

On Lorentz spacetimes of constant curvature

2. The pseudo-Riemannian geometry of

3. Contracting maps and properly discontinuous actions

4. Main results

On the asymptotic behavior of complex earthquakes and Teichmüller disks

2. Background

3. Preliminaries

4. Proof of Theorem 1.1

5. Plumbing disks and Theorem 1.2

Characteristically Simple Beauville Groups, I: Cartesian Powers of Alternating Groups

2. Beauville surfaces and structures

3. Generating cartesian powers

4. Evaluating ₂( ), ₂( ) and ₂( )

5. Beauville structures in cartesian powers

6. Primitive permutation groups

7. Small alternating groups

8. Larger alternating groups

Relatively Hyperbolic Spaces

2. Hyperbolicity and Nearest Point Projections

3. Electric Geometry

4. Application

Complex hyperbolic free groups with many parabolic elements

2. Fixed point tetrahedra of thrice punctured sphere groups

3. Constructing thrice punctured sphere groups from tetrahedra

4. Thrice punctured sphere groups with a three-fold symmetry.

5. Discreteness

On Fatou components and omitted values

2. Implications of an omitted value

3. The Result and its Proof

Some dynamical properties of certain meromorphic functions

2. Notations

3. Basic Dynamical Properties of _{ }

4. The Dynamic Planes of the Function ∈

Back Cover.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references at the end of each chapters.

Description based on print version record.

ISBN:

1-4704-2343-X