Guts of surfaces and the colored Jones polynomial:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Schriftenreihe: | Lecture notes in mathematics
2069 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | X, 170 S. Ill. |
| ISBN: | 364233301X 9783642333019 |
Internformat
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Datensatz im Suchindex
| _version_ | 1807954872248565760 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 HISTORY AND MOTIVATION 1
1.2 STATE GRAPHS, AND STATE SURFACES FAR FROM FIBERS 4
1.3 WHICH LINKS ARE SEMI-ADEQUATE? 7
1.4 ESSENTIAL SURFACES AND COLORED JONES POLYNOMIALS 9
1.5 VOLUME BOUNDS FROM TOPOLOGY AND COMBINATORICS 12
1.6 ORGANIZATION 13
2 DECOMPOSITION INTO 3-BALLS 17
2.1 STATE CIRCLES AND STATE SURFACES 17
2.2 DECOMPOSITION INTO TOPOLOGICAL BALLS 2 0
2.3 PRIMENESS 26
2.4 GENERALIZATIONS TO OTHER STATES 30
3 IDEAL POLYHEDRA 35
3.1 BUILDING BLOCKS O F SHADED FACES 36
3.2 STAIRS AND ARCS IN SHADED FACES 37
3.3 BIGONS AND COMPRESSION DISKS 45
3.4 IDEAL POLYHEDRA FOR CR-HOMOGENEOUS DIAGRAMS 48
4 /-BUNDLES AND ESSENTIAL PRODUCT DISKS 53
4.1 MAXIMAL/-BUNDLES 53
4.2 NORMAL SQUARES AND GLUINGS 56
4.3 PARABOLICALLY COMPRESSING NORMAL SQUARES 62
4.4 /-BUNDLES ARE SPANNED BY ESSENTIAL PRODUCT DISKS 67
4.5 THE A-ADEQUATE, CR-HOMOGENEOUS SETTING 71
5 GUTS AND FIBERS 73
5.1 SIMPLE AND NON-SIMPLE DISKS 73
5.2 CHOOSING A SPANNING SET 77
5.3 DETECTING FIBERS 82
HTTP://D-NB.INFO/1025058895
IMAGE 2
X CONTENTS
5.4 COMPUTING THE GUTS 83
5.5 MODIFICATIONS O F THE DIAGRAM 86
5.6 THE A-ADEQUATE, A-HOMOGENEOUS SETTING 89
6 RECOGNIZING ESSENTIAL PRODUCT DISKS 91
6.1 2-EDGE LOOPS AND ESSENTIAL PRODUCT DISKS 91
6.2 OUTLINE AND FIRST STEP O F PROOF 96
6.3 STEP 2: ANALYSIS NEAR VERTICES 97
6.4 STEP 3: BUILDING STAIRCASES 102
6.5 STEP 4: INSIDE NON-PRIME ARCS 107
7 DIAGRAMS WITHOUT NON-PRIME ARCS 1 09
7.1 MAPPING EPDS TO 2-EDGE LOOPS 110
7.2 A FOUR-TO-ONE MAPPING 114
7.3 ESTIMATING THE SIZE O F E C 117
8 MONTESINOS LINKS 119
8.1 PRELIMINARIES 119
8.2 POLYHEDRAL DECOMPOSITION 123
8.3 TWO-EDGE LOOPS AND ESSENTIAL PRODUCT DISKS 128
8.4 EXCLUDING COMPLEX DISKS 131
9 APPLICATIONS 139
9.1 VOLUME BOUNDS FOR HYPERBOLIC LINKS 139
9.2 VOLUMES O F MONTESINOS LINKS 144
9.3 ESSENTIAL SURFACES AND COLORED JONES POLYNOMIALS 149
9.4 HYPERBOLIC VOLUME AND COLORED JONES POLYNOMIALS 152
10 DISCUSSION AND QUESTIONS 155
10.1 EFFICIENT DIAGRAMS 155
10.2 CONTROL OVER SURFACES 157
10.3 OTHER STATES 159
10.4 A COARSE VOLUME CONJECTURE 159
REFERENCES 1 63
INDEX 1 67 |
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| author | Futer, David Kalfagianni, Efstratia Purcell, Jessica |
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| dewey-full | 514.2242 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2242 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| isbn | 364233301X 9783642333019 |
| language | English |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Futer, David Verfasser (DE-588)102984190X aut Guts of surfaces and the colored Jones polynomial David Futer ; Efstratia Kalfagianni ; Jessica Purcell Berlin [u.a.] Springer 2013 X, 170 S. Ill. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2069 Knoten Mathematik (DE-588)4164314-8 gnd rswk-swf Niederdimensionale Topologie (DE-588)4280826-1 gnd rswk-swf Knoten Mathematik (DE-588)4164314-8 s Niederdimensionale Topologie (DE-588)4280826-1 s DE-604 Kalfagianni, Efstratia Verfasser aut Purcell, Jessica Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-33302-6 Lecture notes in mathematics 2069 (DE-604)BV000676446 2069 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4099793&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025670908&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Futer, David Kalfagianni, Efstratia Purcell, Jessica Guts of surfaces and the colored Jones polynomial Lecture notes in mathematics Knoten Mathematik (DE-588)4164314-8 gnd Niederdimensionale Topologie (DE-588)4280826-1 gnd |
| subject_GND | (DE-588)4164314-8 (DE-588)4280826-1 |
| title | Guts of surfaces and the colored Jones polynomial |
| title_auth | Guts of surfaces and the colored Jones polynomial |
| title_exact_search | Guts of surfaces and the colored Jones polynomial |
| title_full | Guts of surfaces and the colored Jones polynomial David Futer ; Efstratia Kalfagianni ; Jessica Purcell |
| title_fullStr | Guts of surfaces and the colored Jones polynomial David Futer ; Efstratia Kalfagianni ; Jessica Purcell |
| title_full_unstemmed | Guts of surfaces and the colored Jones polynomial David Futer ; Efstratia Kalfagianni ; Jessica Purcell |
| title_short | Guts of surfaces and the colored Jones polynomial |
| title_sort | guts of surfaces and the colored jones polynomial |
| topic | Knoten Mathematik (DE-588)4164314-8 gnd Niederdimensionale Topologie (DE-588)4280826-1 gnd |
| topic_facet | Knoten Mathematik Niederdimensionale Topologie |
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