Coverart for item
The Resource 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]

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]

Label
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
Introductory lectures on knot theory
Title remainder
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
Statement of responsibility
editors, Louis H. Kauffman [and others]
Contributor
Subject
Genre
Language
eng
Summary
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
Member of
Cataloging source
N$T
Dewey number
514.2242
Illustrations
illustrations
Index
no index present
LC call number
QA612.2
LC item number
.I67 2012eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
  • 1945-
  • 2009
http://library.link/vocab/relatedWorkOrContributorName
  • Kauffman, Louis H.
  • Abdus Salam International Centre for Theoretical Physics
  • Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology
Series statement
Series on knots and everything
Series volume
v. 46
http://library.link/vocab/subjectName
  • Knot theory
  • MATHEMATICS
  • Knot theory
Label
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]
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
777561703
Dimensions
unknown
Extent
1 online resource (xi, 519 pages)
File format
unknown
Form of item
online
Isbn
9789814313001
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)777561703
Label
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]
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
777561703
Dimensions
unknown
Extent
1 online resource (xi, 519 pages)
File format
unknown
Form of item
online
Isbn
9789814313001
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)777561703

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