Kooperativer Bibliotheksverbund

UID:

Format: XVII, 427 S. : , Ill.

Edition: 1. publ.

ISBN: 978-0-521-83974-7 , 0-521-83974-2

Content: We live in a three-dimensional space; what sort of space is it? Can we build it from simple geometric objects? The answers to such questions have been found in the last 30 years, and Outer Circles describes the basic mathematics needed for those answers as well as making clear the grand design of the subject of hyperbolic manifolds as a whole. The purpose of Outer Circles is to provide an account of the contemporary theory, accessible to those with minimal formal background in topology, hyperbolic geometry, and complex analysis. The text explains what is needed, and provides the expertise to use the primary tools to arrive at a thorough understanding of the big picture. This picture is further filled out by numerous exercises and expositions at the ends of the chapters and is complemented by a profusion of high quality illustrations. There is an extensive bibliography for further study.

Language: English

Subjects: Mathematics

Keywords: Hyperbolische Mannigfaltigkeit ; Dimension 3 ; Hyperbolische Geometrie

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016029653&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

URL: Inhaltsverzeichnis

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016029653&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

URL: Inhaltsverzeichnis

URL: Inhaltstext

UID:

Format: 1 online resource (xvii, 427 pages) : , digital, PDF file(s).

Edition: 1st ed.

ISBN: 1-107-17500-3 , 1-280-91706-7 , 9786610917068 , 0-511-28965-0 , 0-511-29025-X , 0-511-28833-6 , 0-511-32218-6 , 0-511-61891-3 , 0-511-28901-4

Content: We live in a three-dimensional space; what sort of space is it? Can we build it from simple geometric objects? The answers to such questions have been found in the last 30 years, and Outer Circles describes the basic mathematics needed for those answers as well as making clear the grand design of the subject of hyperbolic manifolds as a whole. The purpose of Outer Circles is to provide an account of the contemporary theory, accessible to those with minimal formal background in topology, hyperbolic geometry, and complex analysis. The text explains what is needed, and provides the expertise to use the primary tools to arrive at a thorough understanding of the big picture. This picture is further filled out by numerous exercises and expositions at the ends of the chapters and is complemented by a profusion of high quality illustrations. There is an extensive bibliography for further study.

Note: Title from publisher's bibliographic system (viewed on 01 Feb 2016). , Cover; Half-title; Title; Copyright; Dedication; Contents; List of Illustrations; Preface; 1 Hyperbolic space and its isometries; 2 Discrete groups; 3 Properties of hyperbolic manifolds; 4 Algebraic and geometric convergence; 5 Deformation spaces and the ends of manifolds; 6 Hyperbolization; 7 Line geometry; 8 Right hexagons and hyperbolic trigonometry; Bibliography; Index , English

Additional Edition: ISBN 0-521-83974-2

Language: English

URL: Volltext

URL: Inhaltstext

URL: https://doi.org/10.1017/CBO9780511618918

UID:

Format: 1 online resource (xviii, 515 pages) : , digital, PDF file(s).

ISBN: 1-316-43039-1 , 1-316-43536-9 , 1-316-33777-4

Content: Over the past three decades there has been a total revolution in the classic branch of mathematics called 3-dimensional topology, namely the discovery that most solid 3-dimensional shapes are hyperbolic 3-manifolds. This book introduces and explains hyperbolic geometry and hyperbolic 3- and 2-dimensional manifolds in the first two chapters and then goes on to develop the subject. The author discusses the profound discoveries of the astonishing features of these 3-manifolds, helping the reader to understand them without going into long, detailed formal proofs. The book is heavily illustrated with pictures, mostly in color, that help explain the manifold properties described in the text. Each chapter ends with a set of exercises and explorations that both challenge the reader to prove assertions made in the text, and suggest further topics to explore that bring additional insight. There is an extensive index and bibliography.

Note: Title from publisher's bibliographic system (viewed on 05 Jan 2016). , Cover -- Half-title page -- Frontis piece -- Title page -- Copyright page -- Dedication -- Contents -- List of Illustrations -- Preface -- 1 Hyperbolic space and its isometries -- 1.1 Möbius transformations -- 1.2 Hyperbolic geometry -- 1.2.1 The hyperbolic plane -- 1.2.2 Hyperbolic space -- 1.3 The circle or sphere at infinity -- 1.4 Gaussian curvature -- 1.5 Further properties of Möbius transformations -- 1.5.1 Commutativity -- 1.5.2 Isometric circles and planes -- 1.5.3 Trace identities -- 1.6 Exercises and explorations -- 2 Discrete groups -- 2.1 Convergence of Möbius transformations -- 2.1.1 Some group terminology -- 2.2 Discreteness -- 2.3 Elementary discrete groups -- 2.4 Kleinian groups -- 2.4.1 The limit set Λ (G) -- 2.4.2 The ordinary (regular, discontinuity) set Ω (G) -- 2.5 Quotient manifolds and orbifolds -- 2.5.1 Covering surfaces and manifolds -- 2.5.2 Orbifolds -- 2.5.3 The conformal boundary -- 2.6 Two fundamental algebraic theorems -- 2.7 Introduction to Riemann surfaces and their uniformization -- 2.8 Fuchsian and Schottky groups -- 2.8.1 Handlebodies -- 2.9 Riemannian metrics and quasiconformal mappings -- 2.10 Teichmüller spaces of Riemann surfaces -- 2.10.1 Teichmüller mappings -- 2.11 The mapping class group MCG(R) -- 2.11.1 Dehn twists -- 2.11.2 The action of MCG(R) on R and Teich(R) -- 2.11.3 The complex structure of Teich(R) -- 2.12 Exercises and explorations -- 2.12.1 Summary of group properties -- 3 Properties of hyperbolic manifolds -- 3.1 The Ahlfors Finiteness Theorem -- 3.2 Tubes and horoballs -- 3.3 Universal properties in hyperbolic 3-manifolds and orbifolds -- 3.4 The thick/thin decomposition of a manifold -- 3.5 Fundamental polyhedra -- 3.5.1 The Ford fundamental region and polyhedron -- 3.5.2 Poincaré's Theorem -- 3.5.3 The Cayley graph dual to tessellation -- 3.6 Geometric finiteness -- 3.6.1 Finite volume. , 3.7 Three-manifold surgery -- 3.7.1 Compressible and incompressible boundary -- 3.7.2 Extensions ∂M→M -- 3.8 Quasifuchsian groups -- 3.8.1 Simultaneous uniformization -- 3.9 Geodesic and measured geodesic laminations -- 3.9.1 Geodesic laminations -- 3.9.2 Measured geodesic laminations -- 3.9.3 Geometric intersection numbers -- 3.9.4 Length of measured laminations -- 3.10 The convex hull of the limit set -- 3.10.1 The bending measure -- 3.10.2 Pleated surfaces -- 3.11 The convex core -- 3.11.1 Length estimates for the convex core boundary -- 3.11.2 Bending measures on convex core boundary -- 3.12 The compact and relative compact core -- 3.13 Rigidity of hyperbolic 3-manifolds -- 3.14 Exercises and explorations -- 4 Algebraic and geometric convergence -- 4.1 Algebraic convergence -- 4.2 Geometric convergence -- 4.3 Polyhedral convergence -- 4.4 The geometric limit -- 4.5 Sequences of limit sets and regions of discontinuity -- 4.5.1 Hausdorff and Carathéodory convergence -- 4.5.2 Convergence of groups and regular sets -- 4.6 New parabolics -- 4.7 Acylindrical manifolds -- 4.8 Dehn filling and Dehn surgery -- 4.9 The prototypical example -- 4.10 Manifolds of finite volume -- 4.10.1 The Dehn Surgery Theorem -- 4.10.2 Sequences of volumes -- 4.10.3 Well ordering of volumes -- 4.10.4 Minimum volumes -- 4.11 Exercises and explorations -- 5 Deformation spaces and the ends of manifolds -- 5.1 The representation variety -- 5.1.1 The discreteness locus -- 5.1.2 The quasiconformal deformation space T(G) -- 5.2 Homotopy equivalence -- 5.2.1 Components of the discreteness locus -- 5.3 The quasiconformal deformation space boundary -- 5.3.1 Bumping and self-bumping -- 5.4 The three conjectures for geometrically infinite manifolds -- 5.5 Ends of hyperbolic manifolds -- 5.6 Tame manifolds -- 5.7 The Ending Lamination Theorem -- 5.8 The Double Limit Theorem. , 5.9 The Density Theorem -- 5.10 Bers slices -- 5.11 The quasifuchsian space boundary -- 5.11.1 The Bers (analytic) boundary -- 5.11.2 The Thurston (geometric) boundary -- 5.12 Examples of geometric limits at the Bers boundary -- 5.13 Classification of the geometric limits -- 5.14 Cannon-Thurston mappings -- 5.14.1 The Cannon-Thurston Theorem -- 5.14.2 Cannon-Thurston mappings and local connectivity -- 5.15 Exercises and explorations -- 6 Hyperbolization -- 6.1 Hyperbolic manifolds that fiber over a circle -- 6.1.1 Automorphisms of surfaces -- 6.1.2 Pseudo-Anosov mappings -- 6.1.3 The space of hyperbolic metrics -- 6.1.4 Fibering -- 6.2 Hyperbolic gluing boundary components -- 6.2.1 Skinning a bordered manifold -- 6.2.2 Totally geodesic boundary -- 6.2.3 Gluing boundary components -- 6.2.4 The Bounded Image Theorem -- 6.3 Hyperbolization of 3-manifolds -- 6.3.1 Review of definitions in 3-manifold topology -- 6.3.2 Hyperbolization -- 6.4 The three big conjectures, now theorems, for closed manifolds -- 6.4.1 Surface subgroups of π[sub(1)](M(G)) =G -- 6.4.2 Remarks on the proof of VHT and VFT: Cubulation -- 6.4.3 Prior computational evidence -- 6.5 Geometrization -- 6.6 Hyperbolic knots and links -- 6.6.1 Knot complements -- 6.6.2 Link complements -- 6.7 Computation of hyperbolic manifolds -- 6.8 The Orbifold Theorem -- 6.9 Exercises and explorations -- 7 Line geometry -- 7.1 Half-rotations -- 7.2 The Lie product -- 7.3 Square roots -- 7.4 Complex distance -- 7.5 Complex distance and line geometry -- 7.6 Exercises and explorations -- 8 Right hexagons and hyperbolic trigonometry -- 8.1 Generic right hexagons -- 8.2 The sine and cosine laws -- 8.3 Degenerate right hexagons -- 8.4 Formulas for triangles, quadrilaterals, and pentagons -- 8.5 Exercises and explorations -- Bibliography -- Index. , English

Additional Edition: ISBN 1-107-11674-0

Language: English

URL: Volltext  (URL des Erstveröffentlichers)

URL: Volltext  (lizenzpflichtig)

URL: Inhaltstext

URL: https://doi.org/10.1017/CBO9781316337776

UID:

Format: 32 S.

Series Statement: Annales Academiae Scientiarum Fennicae : Series A. I, Mathematica 359

Note: Literaturverz. S. 32. - Einzelaufnahme eines Zeitschr.-H.

Language: English

UID:

Format: xviii, 515 Seiten , Illustrationen, Diagramme

Edition: Second edition

ISBN: 9781107116740

Uniform Title: Outer circles

Note: Second edition of Outer circles, which has changed title to: Hyperbolic manifolds. - Includes bibliographical references and index

Language: English

Subjects: Mathematics

Keywords: Hyperbolische Mannigfaltigkeit

URL: Contributor biographical information

URL: Publisher description

URL: Table of contents only

URL: Autorenbiografie

URL: Verlagsangaben

URL: Inhaltstext

UID:

Format: 1 Online-Ressource (xvi, 218 Seiten) : , Illustrationen, Diagramme.

Edition: Reprinted

ISBN: 978-1-4704-1248-7

Series Statement: Mathematical surveys and monographs Volume 21

Note: Aus dem Vorwort:"... international conference at Purdue University during the week of March 11 - 14, 1985: the Symposium on the Occasion of the Proof of the Bieberbach Conjecture."

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 0-8218-1521-0

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-0-8218-1521-2

Language: English

Subjects: Mathematics

Keywords: Bieberbach-Vermutung ; Konferenzschrift ; Konferenzschrift

DOI: 10.1090/surv/021

URL: Volltext  (URL des Erstveröffentlichers)

URL: Volltext  (URL des Erstveröffentlichers)

Author information: Duren, Peter L., 1935-

UID:

Format: 32 S.

Series Statement: Annales Academiae Scientiarum Fennicae : Series A. I, Mathematica 359

Note: Literaturverz. S. 32. - Einzelaufnahme eines Zeitschr.-H.

In: no:188

Language: English

UID:

Format: xvii, 427 p. : , ill. (some col.)

Edition: Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.

Language: English

Keywords: Electronic books.

URL: Click to View

UID:

Format: 1 online resource (xii, 335 pages) : , digital, PDF file(s).

ISBN: 1-107-14225-3 , 1-139-10698-8 , 1-283-29551-2 , 1-139-12201-0 , 9786613295514 , 1-139-11627-4 , 1-139-11191-4 , 1-139-12693-8 , 1-139-11410-7

Series Statement: London Mathematical Society lecture note series ; 328

Uniform Title: Low-dimensional topology and Kleinian groups.

Content: Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.

Note: Selected papers presented at two symposia held in 1984 at the Universities of Warwick and Durham and originally published in: Low-dimensional topology and Kleinian groups. c1986. (London Mathematical Society lecture note series ; 112), and Analytic and geometric aspects of hyperbolic space. c1987. (London Mathematical Society lecture note series ; 111). , Preface -- Preface 2005 -- Notes on notes of Thurston / R.D. Canary, D.B.A. Epstein, P.L. Green -- Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated survaces / D.B.A. Epstein, A. Marden -- Earthquakes in 2-dimensional hyperbolic geometry / W.P. Thurston -- Lectures on measures on limit sets of Kleinian groups / S.J. Patterson. , English

Additional Edition: ISBN 0-521-61558-5

Language: English

UID:

Format: 1 online resource (452 p.)

ISBN: 9781400881642

Series Statement: Annals of Mathematics Studies ; 79

Content: Study 79 contains a collection of papers presented at the Conference on Discontinuous Groups and Ricmann Surfaces at the University of Maryland, May 21-25, 1973. The papers, by leading authorities, deal mainly with Fuchsian and Kleinian groups, Teichmüller spaces, Jacobian varieties, and quasiconformal mappings. These topics are intertwined, representing a common meeting of algebra, geometry, and analysis.

Note: Frontmatter -- , PREFACE -- , CONTENTS -- , CONSTRUCT ABILITY AND BERS STABILITY OF KLEINIAN GROUPS -- , ALGEBRAIC CURVES AND HALF-CANONICAL LINEAR SERIES -- , SUFFICIENT CONDITIONS FOR QUASI-CONFORMAL EXTENSION -- , FUNDAMENTAL DOMAINS FOR KLEINIAN GROUPS -- , SPACES OF DEGENERATING RIEMANN SURFACES -- , MAPPING CLASS GROUPS OF SURFACES: A SURVEY -- , A NOTE ON L2 ( Γ G ) -- , ON THE OUTRADIUS OF FINITE-DIMENSIONAL TEICHMÜLLER SPACES -- , SOME DIRECT LIMITS OF PRIMITIVE HOMOTOPY WORDS AND OF MARKOFF GEODESICS -- , ON THE CARATHÉODORY METRIC IN TEICHMÜLLER SPACES -- , SOME REFINEMENTS OF THE POINCARÉ PERIOD RELATION -- , REMARKS ON AUTOMORPHISMS OF COMPACT RIEMANN SURFACES -- , THE STRUCTURE OF PSL2(R );R , THE RING OF INTEGERS IN A EUCLIDEAN QUADRATIC IMAGINARY NUMBER FIELD -- , QUASI-CONFORMAL MAPPINGS AND LEBESGUE DENSITY -- , ON THE MODULI OF COMPACT RIEMANN SURFACES WITH A FINITE NUMBER OF PUNCTURES -- , MAXIMAL GROUPS AND SIGNATURES -- , COMMENSURABLE GROUPS OF MOEBIUS TRANSFORMATIONS -- , CHABAUTY SPACES OF DISCRETE GROUPS -- , MONODROMY GROUPS AND LINEARLY POLYMORPHIC FUNCTIONS -- , COLLARS ON RIEMANN SURFACES -- , DEFORMATIONS OF CERTAIN COMPLEX MANIFOLDS -- , ON THE A (Γ ) ⊂ Bq(Γ ) CONJECTURE FOR INFINITELY GENERATED GROUPS -- , THE FUNDAMENTAL GROUPS OF CERTAIN SUBGROUP SPACES -- , MODULAR GROUPS AND FIBER SPACES OVER TEICHMÜLLER SPACES -- , UNIVERSAL PROPERTIES OF FUCHSIAN GROUPS IN THE POINCARÉ METRIC -- , REMARKS ON COMPLEX MULTIPLICATION AND SINGULAR RIEMANN MATRICES -- , INTERSECTIONS OF COMPONENT SUBGROUPS OF KLEINIAN GROUPS -- , POLYNOMIAL APPROXIMATION IN THE BERS SPACES -- , SIMPLE ILLUSTRATIONS OF THE USES OF EXPLICIT COMPUTATION OF THETA CONSTANTS -- , ON THE RELATION BETWEEN LOCAL AND GLOBAL PROPERTIES OF BOUNDARY VALUES FOR EXTREMAL QUASI-CONFORMAL MAPPINGS -- , SYMMETRIC EMBEDDINGS OF RIEMANN SURFACES -- , ON THE TRAJECTORY STRUCTURE OF QUADRATIC DIFFERENTIALS -- , THE MAXIMAL INSCRIBED BALL OF A FUCHSIAN GROUP -- , Backmatter , In English.

Language: English

DOI: 10.1515/9781400881642

URL: https://doi.org/10.1515/9781400881642

URL: https://www.degruyter.com/isbn/9781400881642

URL: https://doi.org/10.1515/9781400881642

URL: https://www.degruyter.com/isbn/9781400881642