Introductory lectures on knot theory :: selected lectures presented at the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology, ICTP, Trieste, Italy, 11-29 May 2009 /
This volume consists primarily of survey papers that evolved from the lectures given in the school portion of the meeting and selected papers from the conference. Knot theory is a very special topological subject: the classification of embeddings of a circle or collection of circles into three-dimen...
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| Format: | Elektronisch Tagungsbericht E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, NJ :
World Scientific,
©2012.
|
| Schriftenreihe: | K & E series on knots and everything ;
v. 46. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This volume consists primarily of survey papers that evolved from the lectures given in the school portion of the meeting and selected papers from the conference. Knot theory is a very special topological subject: the classification of embeddings of a circle or collection of circles into three-dimensional space. This is a classical topological problem and a special case of the general placement problem: Understanding the embeddings of a space X in another space Y. There have been exciting new developments in the area of knot theory and 3-manifold topology in the last 25 years. From the Jones, Homflypt and Kauffman polynomials, quantum invariants of 3-manifolds, through, Vassiliev invariants, topological quantum field theories, to relations with gauge theory type invariants in 4-dimensional topology. More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book. It is a remarkable fact that knot theory, while very special in its problematic form, involves ideas and techniques that involve and inform much of mathematics and theoretical physics. The subject has significant applications and relations with biology, physics, combinatorics, algebra and the theory of computation. The summer school on which this book is based contained excellent lectures on the many aspects of applications of knot theory. This book gives an in-depth survey of the state of the art of present day knot theory and its applications. |
| Beschreibung: | 1 online resource (xi, 519 pages) : illustrations |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9789814313001 9814313009 |
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| contents | On the unification of quantum 3-manifold invariants / A. Beliakova and T. Le -- A survey of quandle ideas / J. Scott Carter -- Combinatorics of Vassiliev invariants / S. Chmutov -- Braid order, sets, and knots / P. Dehornoy -- Finding knot invariants from diagram colouring / R. Fenn -- Exceptional Dehn filling / C. McA Gordon -- Graph-links / D.P. Ilyutko and V.O. Manturov -- Diagrammatic knot properties and invariants / S.V. Jablan and R. Sazdanovic -- Hard unknots and collapsing tangles / L.H. Kauffman and S. Lambropoulou -- Khovanov homology / L.H. Kauffman -- Braid equivalences and the L-moves / S. Lambropoulou -- Free knots and parity / V.O. Manturov -- Physical knot theory: an introduction to the study of the influence of knotting on the spatial characteristics of polymers / K.C. Millett -- Knots, satellites and quantum groups / H.R. Morton -- The Trieste look at knot theory / J.H. Przytycki -- Detection of chirality and mutations of knots and links / R. Pichai -- Physical knot theory: the study of sizes and shapes of polymers / E.J. Rawdon -- Derivation and interpretation of the Gauss linking number / R.L. Ricca and B. Nipoti. |
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| series | K & E series on knots and everything ; |
| series2 | Series on knots and everything ; |
| spelling | Introductory lectures on knot theory : selected lectures presented at the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology, ICTP, Trieste, Italy, 11-29 May 2009 / editors, Louis H. Kauffman [and others]. Singapore ; Hackensack, NJ : World Scientific, ©2012. 1 online resource (xi, 519 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Series on knots and everything ; v. 46 Includes bibliographical references. Print version record. On the unification of quantum 3-manifold invariants / A. Beliakova and T. Le -- A survey of quandle ideas / J. Scott Carter -- Combinatorics of Vassiliev invariants / S. Chmutov -- Braid order, sets, and knots / P. Dehornoy -- Finding knot invariants from diagram colouring / R. Fenn -- Exceptional Dehn filling / C. McA Gordon -- Graph-links / D.P. Ilyutko and V.O. Manturov -- Diagrammatic knot properties and invariants / S.V. Jablan and R. Sazdanovic -- Hard unknots and collapsing tangles / L.H. Kauffman and S. Lambropoulou -- Khovanov homology / L.H. Kauffman -- Braid equivalences and the L-moves / S. Lambropoulou -- Free knots and parity / V.O. Manturov -- Physical knot theory: an introduction to the study of the influence of knotting on the spatial characteristics of polymers / K.C. Millett -- Knots, satellites and quantum groups / H.R. Morton -- The Trieste look at knot theory / J.H. Przytycki -- Detection of chirality and mutations of knots and links / R. Pichai -- Physical knot theory: the study of sizes and shapes of polymers / E.J. Rawdon -- Derivation and interpretation of the Gauss linking number / R.L. Ricca and B. Nipoti. This volume consists primarily of survey papers that evolved from the lectures given in the school portion of the meeting and selected papers from the conference. Knot theory is a very special topological subject: the classification of embeddings of a circle or collection of circles into three-dimensional space. This is a classical topological problem and a special case of the general placement problem: Understanding the embeddings of a space X in another space Y. There have been exciting new developments in the area of knot theory and 3-manifold topology in the last 25 years. From the Jones, Homflypt and Kauffman polynomials, quantum invariants of 3-manifolds, through, Vassiliev invariants, topological quantum field theories, to relations with gauge theory type invariants in 4-dimensional topology. More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book. It is a remarkable fact that knot theory, while very special in its problematic form, involves ideas and techniques that involve and inform much of mathematics and theoretical physics. The subject has significant applications and relations with biology, physics, combinatorics, algebra and the theory of computation. The summer school on which this book is based contained excellent lectures on the many aspects of applications of knot theory. This book gives an in-depth survey of the state of the art of present day knot theory and its applications. Knot theory Congresses. Théorie des nuds Congrès. MATHEMATICS Topology. bisacsh Knot theory fast Conference papers and proceedings fast Kauffman, Louis H., 1945- https://id.oclc.org/worldcat/entity/E39PBJg4qXPkDXqXP9QGGHkMT3 http://id.loc.gov/authorities/names/n82220843 Abdus Salam International Centre for Theoretical Physics. http://id.loc.gov/authorities/names/n99031803 Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology (2009 : International Centre for Theoretical Physics, Trieste, Italy) has work: Introductory lectures on knot theory (Text) https://id.oclc.org/worldcat/entity/E39PCGX3C3Pf9HFj8vDChPpbQy https://id.oclc.org/worldcat/ontology/hasWork Print version: Introductory lectures on knot theory. Singapore ; Hackensack, NJ : World Scientific, ©2012 9789814307994 (OCoLC)587219919 K & E series on knots and everything ; v. 46. http://id.loc.gov/authorities/names/n91052105 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=426457 Volltext |
| spellingShingle | Introductory lectures on knot theory : selected lectures presented at the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology, ICTP, Trieste, Italy, 11-29 May 2009 / K & E series on knots and everything ; On the unification of quantum 3-manifold invariants / A. Beliakova and T. Le -- A survey of quandle ideas / J. Scott Carter -- Combinatorics of Vassiliev invariants / S. Chmutov -- Braid order, sets, and knots / P. Dehornoy -- Finding knot invariants from diagram colouring / R. Fenn -- Exceptional Dehn filling / C. McA Gordon -- Graph-links / D.P. Ilyutko and V.O. Manturov -- Diagrammatic knot properties and invariants / S.V. Jablan and R. Sazdanovic -- Hard unknots and collapsing tangles / L.H. Kauffman and S. Lambropoulou -- Khovanov homology / L.H. Kauffman -- Braid equivalences and the L-moves / S. Lambropoulou -- Free knots and parity / V.O. Manturov -- Physical knot theory: an introduction to the study of the influence of knotting on the spatial characteristics of polymers / K.C. Millett -- Knots, satellites and quantum groups / H.R. Morton -- The Trieste look at knot theory / J.H. Przytycki -- Detection of chirality and mutations of knots and links / R. Pichai -- Physical knot theory: the study of sizes and shapes of polymers / E.J. Rawdon -- Derivation and interpretation of the Gauss linking number / R.L. Ricca and B. Nipoti. Knot theory Congresses. Théorie des nuds Congrès. MATHEMATICS Topology. bisacsh Knot theory fast |
| title | Introductory lectures on knot theory : selected lectures presented at the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology, ICTP, Trieste, Italy, 11-29 May 2009 / |
| title_auth | Introductory lectures on knot theory : selected lectures presented at the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology, ICTP, Trieste, Italy, 11-29 May 2009 / |
| title_exact_search | Introductory lectures on knot theory : selected lectures presented at the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology, ICTP, Trieste, Italy, 11-29 May 2009 / |
| title_full | Introductory lectures on knot theory : selected lectures presented at the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology, ICTP, Trieste, Italy, 11-29 May 2009 / editors, Louis H. Kauffman [and others]. |
| title_fullStr | Introductory lectures on knot theory : selected lectures presented at the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology, ICTP, Trieste, Italy, 11-29 May 2009 / editors, Louis H. Kauffman [and others]. |
| title_full_unstemmed | Introductory lectures on knot theory : selected lectures presented at the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology, ICTP, Trieste, Italy, 11-29 May 2009 / editors, Louis H. Kauffman [and others]. |
| title_short | Introductory lectures on knot theory : |
| title_sort | introductory lectures on knot theory selected lectures presented at the advanced school and conference on knot theory and its applications to physics and biology ictp trieste italy 11 29 may 2009 |
| title_sub | selected lectures presented at the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology, ICTP, Trieste, Italy, 11-29 May 2009 / |
| topic | Knot theory Congresses. Théorie des nuds Congrès. MATHEMATICS Topology. bisacsh Knot theory fast |
| topic_facet | Knot theory Congresses. Théorie des nuds Congrès. MATHEMATICS Topology. Knot theory Conference papers and proceedings |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=426457 |
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