Discontinuous Groups Of Isometries In The Hyperbolic Plane

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Discontinuous Groups of Isometries in the Hyperbolic Plane

Werner Fenchel,Jakob Nielsen
Discontinuous Groups of Isometries in the Hyperbolic Plane Book PDF

Author : Werner Fenchel,Jakob Nielsen
Publisher : Walter de Gruyter
Page : 389 pages
File Size : 50,8 Mb
Release : 2011-05-12
Category : Mathematics
ISBN : 9783110891355

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Discontinuous Groups of Isometries in the Hyperbolic Plane by Werner Fenchel,Jakob Nielsen Pdf

This is an introductory textbook on isometry groups of the hyperbolic plane. Interest in such groups dates back more than 120 years. Examples appear in number theory (modular groups and triangle groups), the theory of elliptic functions, and the theory of linear differential equations in the complex domain (giving rise to the alternative name Fuchsian groups). The current book is based on what became known as the famous Fenchel-Nielsen manuscript. Jakob Nielsen (1890-1959) started this project well before World War II, and his interest arose through his deep investigations on the topology of Riemann surfaces and from the fact that the fundamental group of a surface of genus greater than one is represented by such a discontinuous group. Werner Fenchel (1905-1988) joined the project later and overtook much of the preparation of the manuscript. The present book is special because of its very complete treatment of groups containing reversions and because it avoids the use of matrices to represent Moebius maps. This text is intended for students and researchers in the many areas of mathematics that involve the use of discontinuous groups.

Foundations of Hyperbolic Manifolds

John Ratcliffe
Foundations of Hyperbolic Manifolds Book PDF

Author : John Ratcliffe
Publisher : Springer Science & Business Media
Page : 761 pages
File Size : 47,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475740134

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Foundations of Hyperbolic Manifolds by John Ratcliffe Pdf

This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem.

Generators and Relations in Groups and Geometries

A. Barlotti,E.W. Ellers,P. Plaumann,K. Strambach
Generators and Relations in Groups and Geometries Book PDF

Author : A. Barlotti,E.W. Ellers,P. Plaumann,K. Strambach
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401133821

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Generators and Relations in Groups and Geometries by A. Barlotti,E.W. Ellers,P. Plaumann,K. Strambach Pdf

Every group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generators and relations which can be used to detect the structure of a group. Nevertheless, results in the indicated direction exist. The clue is to ask the right question. Classical geometry is a typical example in which the factorization of a motion into reflections or, more generally, of a collineation into central collineations, supplies valuable information on the geometric and algebraic structure. This mode of investigation has gained momentum since the end of last century. The tradition of geometric-algebraic interplay brought forward two branches of research which are documented in Parts I and II of these Proceedings. Part II deals with the theory of reflection geometry which culminated in Bachmann's work where the geometric information is encoded in properties of the group of motions expressed by relations in the generating involutions. This approach is the backbone of the classification of motion groups for the classical unitary and orthogonal planes. The axioms in this char acterization are natural and plausible. They provoke the study of consequences of subsets of axioms which also yield natural geometries whose exploration is rewarding. Bachmann's central axiom is the three reflection theorem, showing that the number of reflections needed to express a motion is of great importance.

Algebraic Generalizations of Discrete Groups

Benjamin Fine,Gerhard Rosenberger
Algebraic Generalizations of Discrete Groups Book PDF

Author : Benjamin Fine,Gerhard Rosenberger
Publisher : CRC Press
Page : 338 pages
File Size : 44,7 Mb
Release : 1999-07-27
Category : Mathematics
ISBN : 0824703197

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Algebraic Generalizations of Discrete Groups by Benjamin Fine,Gerhard Rosenberger Pdf

A survey of one-relator products of cyclics or groups with a single defining relation, extending the algebraic study of Fuchsian groups to the more general context of one-relator products and related group theoretical considerations. It provides a self-contained account of certain natural generalizations of discrete groups.

Groups St Andrews 2005: Volume 1

C. M. Campbell,M. R. Quick,E. F. Robertson,G. C. Smith
Groups St Andrews 2005 Volume 1 Book PDF

Author : C. M. Campbell,M. R. Quick,E. F. Robertson,G. C. Smith
Publisher : Cambridge University Press
Page : 463 pages
File Size : 50,8 Mb
Release : 2007-01-04
Category : Mathematics
ISBN : 9780521694698

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Groups St Andrews 2005: Volume 1 by C. M. Campbell,M. R. Quick,E. F. Robertson,G. C. Smith Pdf

Selected papers from 'Groups St Andrews 2005' cover a wide spectrum of modern group theory.

Foundations of Hyperbolic Manifolds

John G. Ratcliffe
Foundations of Hyperbolic Manifolds Book PDF

Author : John G. Ratcliffe
Publisher : Springer Nature
Page : 800 pages
File Size : 55,5 Mb
Release : 2019-10-23
Category : Mathematics
ISBN : 9783030315979

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Foundations of Hyperbolic Manifolds by John G. Ratcliffe Pdf

This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately.

Groups '93 Galway/St Andrews: Volume 1

C. M. Campbell,London Mathematical Society
Groups 93 Galway St Andrews Volume 1 Book PDF

Author : C. M. Campbell,London Mathematical Society
Publisher : Cambridge University Press
Page : 320 pages
File Size : 45,9 Mb
Release : 1995-03-16
Category : Mathematics
ISBN : 9780521477499

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Groups '93 Galway/St Andrews: Volume 1 by C. M. Campbell,London Mathematical Society Pdf

Representing the wealth and diversity of group theory for experienced researchers as well as new postgraduates, this two-volume book contains selected papers from the international conference which was held at University College Galway in August 1993.

Natural Communication

Elias Zafiris
Natural Communication Book PDF

Author : Elias Zafiris
Publisher : Birkhäuser
Page : 544 pages
File Size : 53,5 Mb
Release : 2021-03-08
Category : Architecture
ISBN : 9783035620801

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Natural Communication by Elias Zafiris Pdf

In Natural Communication kritisiert der Autor das derzeitige Paradigma der Komplexitätswissenschaften, die Ziele immer spezifisch in den Blick nimmt. Er schlägt eine Alternative vor, die eine grundlegende Architektur der Kommunikation vorstellt. Sein Modell der „natürlichen Kommunikation" schließt moderne theoretische Konzepte aus Mathematik und Physik mit ein, insbesondere der Kategorietheorie und der Quantenmechanik. Er abstrahiert daraus präzise Grundbegriffe, die zu einer terminologischen Basis dieser Theorie führen und die Möglichkeit eröffnen, mit Komplexität neu umzugehen. Der Autor ist davon überzeugt, dass es nur durch einen Blick in die Vergangenheit möglich ist, eine Kontinuität und Kohärenz in unserer gegenwärtigen Denkweise herzustellen, insbesondere in Bezug auf die Komplexität.

Geometry and Dynamics in Gromov Hyperbolic Metric Spaces

Tushar Das,David Simmons,Mariusz Urbański
Geometry and Dynamics in Gromov Hyperbolic Metric Spaces Book PDF

Author : Tushar Das,David Simmons,Mariusz Urbański
Publisher : American Mathematical Soc.
Page : 281 pages
File Size : 43,6 Mb
Release : 2017-04-14
Category : Geometry, Hyperbolic
ISBN : 9781470434656

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Geometry and Dynamics in Gromov Hyperbolic Metric Spaces by Tushar Das,David Simmons,Mariusz Urbański Pdf

This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.

Geometry of Riemann Surfaces

William J. Harvey,Frederick P. Gardiner,Gabino González-Diez,Christos Kourouniotis
Geometry of Riemann Surfaces Book PDF

Author : William J. Harvey,Frederick P. Gardiner,Gabino González-Diez,Christos Kourouniotis
Publisher : Cambridge University Press
Page : 416 pages
File Size : 45,7 Mb
Release : 2010-02-11
Category : Mathematics
ISBN : 9780521733076

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Geometry of Riemann Surfaces by William J. Harvey,Frederick P. Gardiner,Gabino González-Diez,Christos Kourouniotis Pdf

Original research and expert surveys on Riemann surfaces.

Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology

Jens Bölte,Frank Steiner
Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology Book PDF

Author : Jens Bölte,Frank Steiner
Publisher : Cambridge University Press
Page : 285 pages
File Size : 49,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9781107610491

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Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology by Jens Bölte,Frank Steiner Pdf

Leading experts introduce this classical subject with exciting new applications in theoretical physics.

Handbook of Teichmüller Theory

Athanase Papadopoulos
Handbook of Teichm ller Theory Book PDF

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
Page : 888 pages
File Size : 45,8 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190558

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Handbook of Teichmüller Theory by Athanase Papadopoulos Pdf

This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.

Geometry, Topology and Dynamics of Character Varieties

William Goldman
Geometry Topology and Dynamics of Character Varieties Book PDF

Author : William Goldman
Publisher : World Scientific
Page : 362 pages
File Size : 52,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814401364

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Geometry, Topology and Dynamics of Character Varieties by William Goldman Pdf

This book aims to describe, for readers uneducated in science, the development of humanity's desire to know and understand the world around us through the various stages of its development to the present, when science is almost universally recognized - at least in the Western world - as the most reliable way of knowing. The book describes the history of the large-scale exploration of the surface of the earth by sea, beginning with the Vikings and the Chinese, and of the unknown interiors of the American and African continents by foot and horseback. After the invention of the telescope, visual exploration of the surfaces of the Moon and Mars were made possible, and finally a visit to the Moon. The book then turns to our legacy from the ancient Greeks of wanting to understand rather than just know, and why the scientific way of understanding is valued. For concreteness, it relates the lives and accomplishments of six great scientists, four from the nineteenth century and two from the twentieth. Finally, the book explains how chemistry came to be seen as the most basic of the sciences, and then how physics became the most fundamental.

Spectral Geometry

Alex Barnett
Spectral Geometry Book PDF

Author : Alex Barnett
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 46,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821853191

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Spectral Geometry by Alex Barnett Pdf

This volume contains the proceedings of the International Conference on Spectral Geometry, held July 19-23, 2010, at Dartmouth College, Dartmouth, New Hampshire. Eigenvalue problems involving the Laplace operator on manifolds have proven to be a consistently fertile area of geometric analysis with deep connections to number theory, physics, and applied mathematics. Key questions include the measures to which eigenfunctions of the Laplacian on a Riemannian manifold condense in the limit of large eigenvalue, and the extent to which the eigenvalues and eigenfunctions of a manifold encode its geometry. In this volume, research and expository articles, including those of the plenary speakers Peter Sarnak and Victor Guillemin, address the flurry of recent progress in such areas as quantum unique ergodicity, isospectrality, semiclassical measures, the geometry of nodal lines of eigenfunctions, methods of numerical computation, and spectra of quantum graphs. This volume also contains mini-courses on spectral theory for hyperbolic surfaces, semiclassical analysis, and orbifold spectral geometry that prepared the participants, especially graduate students and young researchers, for conference lectures.

Group Theory - Proceedings Of The Biennial Ohio State - Denison Conference

Ronald Solomon,Surinder K Sehgal
Group Theory Proceedings Of The Biennial Ohio State Denison Conference Book PDF

Author : Ronald Solomon,Surinder K Sehgal
Publisher : World Scientific
Page : 350 pages
File Size : 51,5 Mb
Release : 1993-09-30
Category : Electronic
ISBN : 9789814553032

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Group Theory - Proceedings Of The Biennial Ohio State - Denison Conference by Ronald Solomon,Surinder K Sehgal Pdf

This volume is a collection of invited papers on the theory of groups, most of which were presented at the biennial Ohio State-Denison Conference, May 1992, in memory of Hans Zassenhaus. These papers treat important topics in the theory of p-groups, solvable groups, finitely presented groups, arithmetic groups, monodromy groups and the general structure and representation theory of groups. Of particular note are papers by John Walter on root systems, by Leonard Scott on integral equivalence of permutation representations and Alex Turull on generalized Brauer groups.