Low-dimensional geometry: from Euclidean surfaces to hyperbolic knots
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2009]
|
| Schriftenreihe: | Student mathematical library
volume 49 : IAS Park City mathematical subseries |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvi, 384 Seiten Illustrationen, Diagramme |
| ISBN: | 9780821848166 082184816X |
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Datensatz im Suchindex
| _version_ | 1804140309410480128 |
|---|---|
| adam_text | STUDENT MATHEMATICAL LIBRARY 151IAS/PARK CITY MATHEMATICAL SUBSERIES
VOLUME 49 LOW -DIMENSIONAL GEOMETRY FROM EUCLIDEAN SURFACES TO
HYPERBOLIC KNOTS FRANCIS BONAHON AMERICANMATHEMATICAL SOCIETY,
PROVIDENCE, RHODE ISLAND INSTITUTE FORADVANCED STUDY, PRINCETON,NEW
JERSEY TABLE OF CONTENTS TABLE OF CONTENTS VII IAS/PARK CITY MATHEMATICS
INSTITUTE XI PREFACE XIII CHAPTER 1. THE EUCLIDEAN PLANE 1 §1.1.
EUCLIDEAN LENGTH AND DISTANCE 1 §1.2. SHORTEST CURVES 3 §1.3. METRIC
SPACES 3 §1.4. ISOMETRIES 5 EXERCISES FOR CHAPTER 1 7 CHAPTER 2. THE
HYPERBOLIC PLANE 11 §2.1. THE HYPERBOLIC PLANE 11 §2.2. SOME ISOMETRIES
OF THE HYPERBOLIC PLANE 14 §2.3. SHORTEST CURVES IN THE HYPERBOLIC PLANE
17 §2.4. ALL ISOMETRIES OF THE HYPERBOLIC PLANE 23 §2.5. LINEAR AND
ANTILINEAR FRACTIONAL MAPS 27 §2.6. THE HYPERBOLIC NORM 33 §2.7. THE
DISK MODEL FOR THE HYPERBOLIC PLANE 36 VII VIII TABLE OF CONTENTS
EXERCISES FOR CHAPTER 2 39 CHAPTER 3. THE 2-DIMENSIONAL SPHERE 47 §3.1.
THE 2-DIMENSIONAL SPHERE 47 §3.2. SHORTEST CURVES 48 §3.3. ISOMETRIES 49
EXERCISES FOR CHAPTER 3 50 CHAPTER 4. GLUING CONSTRUCTIONS 55 §4.1.
INFORMAL EXAMPLES: THE CYLINDER AND THE TORUS 55 §4.2. MATHEMATICAL
DEFINITION OF GLUINGS AND QUOTIENT SPACES 58 §4.3. GLUING THE EDGES OF A
EUCLIDEAN POLYGON 61 §4.4. PROOFS OF THEOREMS 4.3 AND 4.4 67 §4.5.
GLUING HYPERBOLIC AND SPHERICAL POLYGONS 79 EXERCISES FOR CHAPTER 4 84
CHAPTER 5. GLUING EXAMPLES 89 §5,1. SOME EUCLIDEAN SURFACES 89 §5.2. THE
SURFACE OF GENUS 2 97 §5.3. THE PROJECTIVE PLANE 102 §5.4. THE CYLINDER
AND THE MOBIUS STRIP 103 §5.5. THE ONCE-PUNCTURED TORUS 114 §5.6.
TRIANGULAR PILLOWCASES 125 EXERCISES FOR CHAPTER 5 126 CHAPTER 6.
TESSELLATIONS 133 §6.1. TESSELLATIONS 133 §6.2. COMPLETE METRIC SPACES
134 §6.3. PROM GLUING POLYGON EDGES TO TESSELLATIONS 135 §6.4.
COMPLETENESS AND COMPACTNESS PROPERTIES 147 §6.5. TESSELLATIONS BY
BOUNDED POLYGONS 155 §6.6. TESSELLATIONS BY UNBOUNDED POLYGONS 161 §6.7.
INCOMPLETE HYPERBOLIC SURFACES 163 TABLE OF CONTENTS IX §6.8. POINCARE S
POLYGON THEOREM 169 EXERCISES FOR CHAPTER 6 182 CHAPTER 7. GROUP ACTIONS
AND FUNDAMENTAL DOMAINS 185 §7.1. TRANSFORMATION GROUPS 185 §7.2. GROUP
ACTIONS AND QUOTIENT SPACES 187 §7.3. FUNDAMENTAL DOMAINS 192 §7.4.
DIRICHLET DOMAINS 197 EXERCISES FOR CHAPTER 7 202 CHAPTER 8. THE FAREY
TESSELLATION AND CIRCLE PACKING 207 §8.1. THE FAREY CIRCLE PACKING AND
TESSELLATION 207 §8.2. THE FAREY TESSELLATION AND THE ONCE-PUNCTURED
TORUS 212 §8.3. HOROCIRCLES AND THE FAREY CIRCLE PACKING 214 §8.4.
SHEARING THE FAREY TESSELLATION 217 EXERCISES FOR CHAPTER 8 222 CHAPTER
9. THE 3-DIMENSIONAL HYPERBOLIC SPACE 227 §9.1. THE HYPERBOLIC SPACE 227
§9.2. SHORTEST CURVES IN THE HYPERBOLIC SPACE 230 §9.3. ISOMETRIES OF
THE HYPERBOLIC SPACE 231 §9.4. HYPERBOLIC PLANES AND HOROSPHERES 234
EXERCISES FOR CHAPTER 9 235 CHAPTER 10. KLEINIAN GROUPS 241 §10.1.
BENDING THE FAREY TESSELLATION 241 §10.2. KLEINIAN GROUPS AND THEIR
LIMIT SETS 247 §10.3. FIRST RIGOROUS EXAMPLE: FUCHSIAN GROUPS 252 §10.4.
POINCARE S POLYHEDRON THEOREM 257 §10.5. MORE EXAMPLES OF KLEINIAN
GROUPS 265 §10.6. POINCARE, FUCHS AND KLEIN 283 EXERCISES FOR CHAPTER 10
286 CHAPTER 11. THE FIGURE-EIGHT KNOT COMPLEMENT 293 X TABLE OF CONTENTS
§11.1. ANOTHER CROOKED FAREY TESSELLATION 293 §11.2. ENLARGING THE GROUP
T8 294 §11.3, LIMIT SETS 299 §11.4. THE FIGURE-EIGHT KNOT 303 EXERCISES
FOR CHAPTER 11 312 CHAPTER 12. GEOMETRIZATION THEOREMS IN DIMENSION 3
315 §12.1. KNOTS 315 §12.2. THE GEOMETRIZATIONTHEOREM FOR KNOT
COMPLEMENTS 319 §12.3. MOSTOW S RIGIDITY THEOREM 324 §12.4. FORD DOMAINS
326 §12.5. THE GENERAL GEOMETRIZATION THEOREM 340 EXERCISES FOR CHAPTER
12 351 APPENDIX. TOOL KIT 355 §T.L. ELEMENTARY SET THEORY 355 §T.2.
MAXIMUM, MINIMUM, SUPREMUM, AND INFIMUM 358 §T.3. LIMITS AND CONTINUITY.
LIMITS INVOLVING INFINITY 360 §T.4. COMPLEX NUMBERS 361 SUPPLEMENTAL
BIBLIOGRAPHY AND REFERENCES 365 SUPPLEMENTAL BIBLIOGRAPHY 365 REFERENCES
369 INDEX 377
|
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| isbn | 9780821848166 082184816X |
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| spelling | Bonahon, Francis 1955- Verfasser (DE-588)139634290 aut Low-dimensional geometry from Euclidean surfaces to hyperbolic knots Francis Bonahon Providence, Rhode Island American Mathematical Society [2009] © 2009 xvi, 384 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 49 IAS Park City mathematical subseries Geometry, Hyperbolic Geometry, Plane Knot theory Manifolds (Mathematics) Euklidische Geometrie (DE-588)4137555-5 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Euklidische Geometrie (DE-588)4137555-5 s Hyperbolische Geometrie (DE-588)4161041-6 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1634-8 Student mathematical library volume 49 : IAS Park City mathematical subseries (DE-604)BV013184751 49 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018338770&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bonahon, Francis 1955- Low-dimensional geometry from Euclidean surfaces to hyperbolic knots Student mathematical library Geometry, Hyperbolic Geometry, Plane Knot theory Manifolds (Mathematics) Euklidische Geometrie (DE-588)4137555-5 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| subject_GND | (DE-588)4137555-5 (DE-588)4161041-6 |
| title | Low-dimensional geometry from Euclidean surfaces to hyperbolic knots |
| title_auth | Low-dimensional geometry from Euclidean surfaces to hyperbolic knots |
| title_exact_search | Low-dimensional geometry from Euclidean surfaces to hyperbolic knots |
| title_full | Low-dimensional geometry from Euclidean surfaces to hyperbolic knots Francis Bonahon |
| title_fullStr | Low-dimensional geometry from Euclidean surfaces to hyperbolic knots Francis Bonahon |
| title_full_unstemmed | Low-dimensional geometry from Euclidean surfaces to hyperbolic knots Francis Bonahon |
| title_short | Low-dimensional geometry |
| title_sort | low dimensional geometry from euclidean surfaces to hyperbolic knots |
| title_sub | from Euclidean surfaces to hyperbolic knots |
| topic | Geometry, Hyperbolic Geometry, Plane Knot theory Manifolds (Mathematics) Euklidische Geometrie (DE-588)4137555-5 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| topic_facet | Geometry, Hyperbolic Geometry, Plane Knot theory Manifolds (Mathematics) Euklidische Geometrie Hyperbolische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018338770&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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