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
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| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
c2012
|
| Schriftenreihe: | K & E series on knots and everything
v. 46 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references 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 |
| Beschreibung: | 1 Online-Ressource (xi, 519 p.) |
| ISBN: | 9789814307994 9789814313001 9814307998 9814313009 |
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| 245 | 1 | 0 | |a Introductory lectures on knot theory |b 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 |c editors, Louis H. Kauffman ... [et al.] |
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| 500 | |a 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 | ||
| 500 | |a 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. | ||
| 500 | |a 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. | ||
| 500 | |a 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 | ||
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| 710 | 2 | |a Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology <2009, International Centre for Theoretical Physics, Trieste, Italy> |e Sonstige |4 oth | |
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| 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 ... [et al.] Singapore World Scientific c2012 1 Online-Ressource (xi, 519 p.) txt rdacontent c rdamedia cr rdacarrier K & E series on knots and everything v. 46 Includes bibliographical references 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 MATHEMATICS / Topology bisacsh Knot theory fast Knot theory Congresses Knoten Mathematik (DE-588)4164314-8 gnd rswk-swf Knotentheorie (DE-588)4164318-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Knoten Mathematik (DE-588)4164314-8 s Knotentheorie (DE-588)4164318-5 s 1\p DE-604 Kauffman, Louis H. Sonstige oth Abdus Salam International Centre for Theoretical Physics Sonstige oth Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology <2009, International Centre for Theoretical Physics, Trieste, Italy> Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=426457 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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 MATHEMATICS / Topology bisacsh Knot theory fast Knot theory Congresses Knoten Mathematik (DE-588)4164314-8 gnd Knotentheorie (DE-588)4164318-5 gnd |
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| 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 ... [et al.] |
| 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 ... [et al.] |
| 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 ... [et al.] |
| 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 | MATHEMATICS / Topology bisacsh Knot theory fast Knot theory Congresses Knoten Mathematik (DE-588)4164314-8 gnd Knotentheorie (DE-588)4164318-5 gnd |
| topic_facet | MATHEMATICS / Topology Knot theory Knot theory Congresses Knoten Mathematik Knotentheorie Konferenzschrift |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=426457 |
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