Knot Theory and Its Applications, Krishnendu Gongopadhyay, Rama Mishra

Автор: Li Weiping
Название: Lecture Notes On Knot Invariants
ISBN: 9814675954 ISBN-13(EAN): 9789814675956
Издательство: World Scientific Publishing
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Описание: The volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry.

Автор: M.E. Bozh?y?k
Название: Topics in Knot Theory
ISBN: 0792322851 ISBN-13(EAN): 9780792322856
Издательство: Springer
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Описание: Proceedings of the NATO Advanced Study Institute, Erzurum, Turkey, September 1-12, 1992

Автор: J. P. Levine
Название: Algebraic Structure of Knot Modules
ISBN: 3540097392 ISBN-13(EAN): 9783540097396
Издательство: Springer
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Автор: E. Winkelnkemper; Andrew Ranicki
Название: High-dimensional Knot Theory
ISBN: 3642083293 ISBN-13(EAN): 9783642083297
Издательство: Springer
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Описание: High-dimensional knot theory is the study of the embeddings of n-dimensional manifolds in (n+2)-dimensional manifolds, generalizing the traditional study of knots in the case n=1. The main theme is the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory. Many results in the research literature are thus brought into a single framework, and new results are obtained. The treatment is particularly effective in dealing with open books, which are manifolds with codimension 2 submanifolds such that the complement fibres over a circle. The book concludes with an appendix by E. Winkelnkemper on the history of open books.

Автор: Akio Kawauchi
Название: A Survey of Knot Theory
ISBN: 303489953X ISBN-13(EAN): 9783034899536
Издательство: Springer
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Цена: 93130.00 T
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Описание: Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today`s most recent research results. An indispensable book for everyone concerned with knot theory.

Автор: W.B.Raymond Lickorish
Название: An Introduction to Knot Theory
ISBN: 1461268699 ISBN-13(EAN): 9781461268697
Издательство: Springer
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Описание: This account is an introduction to mathematical knot theory, the theory of knots and links of simple closed curves in three-dimensional space. Knots can be studied at many levels and from many points of view. They can be admired as artifacts of the decorative arts and crafts, or viewed as accessible intimations of a geometrical sophistication that may never be attained. The study of knots can be given some motivation in terms of applications in molecular biology or by reference to paral- lels in equilibrium statistical mechanics or quantum field theory. Here, however, knot theory is considered as part of geometric topology. Motivation for such a topological study of knots is meant to come from a curiosity to know how the ge- ometry of three-dimensional space can be explored by knotting phenomena using precise mathematics. The aim will be to find invariants that distinguish knots, to investigate geometric properties of knots and to see something of the way they interact with more adventurous three-dimensional topology. The book is based on an expanded version of notes for a course for recent graduates in mathematics given at the University of Cambridge; it is intended for others with a similar level of mathematical understanding. In particular, a knowledge of the very basic ideas of the fundamental group and of a simple homology theory is assumed; it is, after all, more important to know about those topics than about the intricacies of knot theory.

Автор: Dale Rolfsen
Название: Knot Theory and Manifolds
ISBN: 3540156801 ISBN-13(EAN): 9783540156802
Издательство: Springer
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Автор: E. Winkelnkemper; Andrew Ranicki
Название: High-dimensional Knot Theory
ISBN: 3540633898 ISBN-13(EAN): 9783540633891
Издательство: Springer
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Цена: 121070.00 T
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Описание: High dimensional knot theory is the study of the embeddings of n-dimensional manifolds in (n+2)-dimensional manifolds, generalizing the traditional study of knots in the case n=1. The main theme is the application of the author`s algebraic theory of surgery.

Автор: Ben Webster
Название: Knot Invariants and Higher Representation Theory
ISBN: 1470426501 ISBN-13(EAN): 9781470426507
Издательство: Mare Nostrum (Eurospan)
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Описание: The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$ and by Mazorchuk-Stroppel and Sussan for $\mathfrak{sl}_n$.