Functorial knot theory: categories of tangles, coherence, categorical deformations, and topological invariants
Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures natural...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2001
|
| Schriftenreihe: | K & E series on knots and everything
v. 26 |
| Schlagworte: | |
| Online-Zugang: | FHN01 URL des Erstveroeffentlichers |
| Zusammenfassung: | Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory. This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low-dimensional topology. The focus then turns to the deformation theory of monoidal categories and the related deformation theory of monoidal functors, which is a proper generalization of Gerstenhaber's deformation theory of associative algebras. These serve as the building blocks for a deformation theory of braided monoidal categories which gives rise to sequences of Vassiliev invariants of framed links, and clarify their interrelations |
| Beschreibung: | 230 p. ill |
| ISBN: | 9789812810465 |
Internformat
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| 520 | |a Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory. This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low-dimensional topology. The focus then turns to the deformation theory of monoidal categories and the related deformation theory of monoidal functors, which is a proper generalization of Gerstenhaber's deformation theory of associative algebras. These serve as the building blocks for a deformation theory of braided monoidal categories which gives rise to sequences of Vassiliev invariants of framed links, and clarify their interrelations | ||
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Datensatz im Suchindex
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| discipline | Mathematik |
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| id | DE-604.BV044636108 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:48Z |
| institution | BVB |
| isbn | 9789812810465 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030034080 |
| oclc_num | 1012670500 |
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| physical | 230 p. ill |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| publisher | World Scientific Pub. Co. |
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| series2 | K & E series on knots and everything |
| spelling | Yetter, David N. Verfasser aut Functorial knot theory categories of tangles, coherence, categorical deformations, and topological invariants David N. Yetter Singapore World Scientific Pub. Co. c2001 230 p. ill txt rdacontent c rdamedia cr rdacarrier K & E series on knots and everything v. 26 Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory. This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low-dimensional topology. The focus then turns to the deformation theory of monoidal categories and the related deformation theory of monoidal functors, which is a proper generalization of Gerstenhaber's deformation theory of associative algebras. These serve as the building blocks for a deformation theory of braided monoidal categories which gives rise to sequences of Vassiliev invariants of framed links, and clarify their interrelations Knot theory Categories (Mathematics) Functor theory Erscheint auch als Druck-Ausgabe 9789810244439 Erscheint auch als Druck-Ausgabe 9810244436 http://www.worldscientific.com/worldscibooks/10.1142/4542#t=toc Verlag URL des Erstveroeffentlichers Volltext |
| spellingShingle | Yetter, David N. Functorial knot theory categories of tangles, coherence, categorical deformations, and topological invariants Knot theory Categories (Mathematics) Functor theory |
| title | Functorial knot theory categories of tangles, coherence, categorical deformations, and topological invariants |
| title_auth | Functorial knot theory categories of tangles, coherence, categorical deformations, and topological invariants |
| title_exact_search | Functorial knot theory categories of tangles, coherence, categorical deformations, and topological invariants |
| title_full | Functorial knot theory categories of tangles, coherence, categorical deformations, and topological invariants David N. Yetter |
| title_fullStr | Functorial knot theory categories of tangles, coherence, categorical deformations, and topological invariants David N. Yetter |
| title_full_unstemmed | Functorial knot theory categories of tangles, coherence, categorical deformations, and topological invariants David N. Yetter |
| title_short | Functorial knot theory |
| title_sort | functorial knot theory categories of tangles coherence categorical deformations and topological invariants |
| title_sub | categories of tangles, coherence, categorical deformations, and topological invariants |
| topic | Knot theory Categories (Mathematics) Functor theory |
| topic_facet | Knot theory Categories (Mathematics) Functor theory |
| url | http://www.worldscientific.com/worldscibooks/10.1142/4542#t=toc |
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