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 ... [et al.], (electronic 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 ... [et al.], (electronic resource)

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 ... [et al.]
Contributor
Subject
Genre
Language
eng
Summary
Annotation
Related
Member of
Cataloging source
BTCTA
Dewey number
514.2242
LC call number
QA612.2
LC item number
.I58 2012
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 Application to Physics and Biology
Series statement
Series on knots and everything
Series volume
v. 46
http://library.link/vocab/subjectName
Knot theory
Summary expansion
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
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 ... [et al.], (electronic resource)
Instantiates
Publication
Bibliography note
Includes bibliographical references
Control code
OCM1bookssj0000646340
Dimensions
24 cm.
Dimensions
unknown
Extent
xi, 519 p.
Isbn
9789814307994
Lccn
2011275636
Other physical details
ill.
Specific material designation
remote
System control number
(WaSeSS)ssj0000646340
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 ... [et al.], (electronic resource)
Publication
Bibliography note
Includes bibliographical references
Control code
OCM1bookssj0000646340
Dimensions
24 cm.
Dimensions
unknown
Extent
xi, 519 p.
Isbn
9789814307994
Lccn
2011275636
Other physical details
ill.
Specific material designation
remote
System control number
(WaSeSS)ssj0000646340

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