Temperley-Lieb recoupling theory and invariants of 3-manifolds:
This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, hi...
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| Hauptverfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[1994]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 134 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2-cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3-gems (graph encoded 3-manifolds) in an approach pioneered by Sostenes Lins. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) |
| Beschreibung: | 1 online resource |
| ISBN: | 9781400882533 |
| DOI: | 10.1515/9781400882533 |
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| 245 | 1 | 0 | |a Temperley-Lieb recoupling theory and invariants of 3-manifolds |c Louis H. Kauffman, Sostenes Lins |
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| 490 | 1 | |a Annals of Mathematics Studies |v number 134 | |
| 500 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) | ||
| 520 | |a This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2-cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3-gems (graph encoded 3-manifolds) in an approach pioneered by Sostenes Lins. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds | ||
| 546 | |a In English | ||
| 650 | 4 | |a Invariants | |
| 650 | 4 | |a Knot theory | |
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Datensatz im Suchindex
| _version_ | 1804176498608832512 |
|---|---|
| any_adam_object | |
| author | Kauffman, Louis H. 1945- Lins, Sóstenes 20. Jht |
| author_GND | (DE-588)134212614 (DE-588)1089221649 |
| author_facet | Kauffman, Louis H. 1945- Lins, Sóstenes 20. Jht |
| author_role | aut aut |
| author_sort | Kauffman, Louis H. 1945- |
| author_variant | l h k lh lhk s l sl |
| building | Verbundindex |
| bvnumber | BV043712513 |
| collection | ZDB-23-DGG ZDB-23-PST |
| ctrlnum | (ZDB-23-DGG)9781400882533 (OCoLC)1165461662 (DE-599)BVBBV043712513 |
| dewey-full | 514/.224 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.224 |
| dewey-search | 514/.224 |
| dewey-sort | 3514 3224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400882533 |
| format | Electronic eBook |
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| id | DE-604.BV043712513 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:33:08Z |
| institution | BVB |
| isbn | 9781400882533 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029124741 |
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| psigel | ZDB-23-DGG ZDB-23-PST |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spelling | Kauffman, Louis H. 1945- (DE-588)134212614 aut Temperley-Lieb recoupling theory and invariants of 3-manifolds Louis H. Kauffman, Sostenes Lins Princeton, NJ Princeton University Press [1994] © 1994 1 online resource txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 134 Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2-cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3-gems (graph encoded 3-manifolds) in an approach pioneered by Sostenes Lins. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds In English Invariants Knot theory Three-manifolds (Topology) Knotentheorie (DE-588)4164318-5 gnd rswk-swf Dimension 3 (DE-588)4321722-9 gnd rswk-swf Invariante (DE-588)4128781-2 gnd rswk-swf Knoten Mathematik (DE-588)4164314-8 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s Knoten Mathematik (DE-588)4164314-8 s Invariante (DE-588)4128781-2 s 1\p DE-604 Knotentheorie (DE-588)4164318-5 s 2\p DE-604 Lins, Sóstenes 20. Jht. (DE-588)1089221649 aut Erscheint auch als Druck-Ausgabe 978-0-691-03640-3 Annals of Mathematics Studies number 134 (DE-604)BV040389493 134 https://doi.org/10.1515/9781400882533?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kauffman, Louis H. 1945- Lins, Sóstenes 20. Jht Temperley-Lieb recoupling theory and invariants of 3-manifolds Annals of Mathematics Studies Invariants Knot theory Three-manifolds (Topology) Knotentheorie (DE-588)4164318-5 gnd Dimension 3 (DE-588)4321722-9 gnd Invariante (DE-588)4128781-2 gnd Knoten Mathematik (DE-588)4164314-8 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| subject_GND | (DE-588)4164318-5 (DE-588)4321722-9 (DE-588)4128781-2 (DE-588)4164314-8 (DE-588)4037379-4 |
| title | Temperley-Lieb recoupling theory and invariants of 3-manifolds |
| title_auth | Temperley-Lieb recoupling theory and invariants of 3-manifolds |
| title_exact_search | Temperley-Lieb recoupling theory and invariants of 3-manifolds |
| title_full | Temperley-Lieb recoupling theory and invariants of 3-manifolds Louis H. Kauffman, Sostenes Lins |
| title_fullStr | Temperley-Lieb recoupling theory and invariants of 3-manifolds Louis H. Kauffman, Sostenes Lins |
| title_full_unstemmed | Temperley-Lieb recoupling theory and invariants of 3-manifolds Louis H. Kauffman, Sostenes Lins |
| title_short | Temperley-Lieb recoupling theory and invariants of 3-manifolds |
| title_sort | temperley lieb recoupling theory and invariants of 3 manifolds |
| topic | Invariants Knot theory Three-manifolds (Topology) Knotentheorie (DE-588)4164318-5 gnd Dimension 3 (DE-588)4321722-9 gnd Invariante (DE-588)4128781-2 gnd Knoten Mathematik (DE-588)4164314-8 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| topic_facet | Invariants Knot theory Three-manifolds (Topology) Knotentheorie Dimension 3 Invariante Knoten Mathematik Mannigfaltigkeit |
| url | https://doi.org/10.1515/9781400882533?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT kauffmanlouish temperleyliebrecouplingtheoryandinvariantsof3manifolds AT linssostenes temperleyliebrecouplingtheoryandinvariantsof3manifolds |