Temperley-Lieb recoupling theory and invariants of 3-manifolds

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Princeton University Press , Princeton, N.J
Knot theory., Three-manifolds (Topology), Invariants (Mathema
Statementby Louis H. Kauffman and Sóstenes L. Lins.
SeriesAnnals of mathematics studies -- no. 134
ContributionsLins, Sóstenes L.
Classifications
LC ClassificationsQA612.2
ID Numbers
Open LibraryOL22236988M
ISBN 100691036411, 0691036403

The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling Temperley-Lieb recoupling theory and invariants of 3-manifolds book is a q-deformation of the SU (2) spin networks of Roger Penrose.

The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants.

The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra.

Description Temperley-Lieb recoupling theory and invariants of 3-manifolds FB2

Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM) - Ebook written by Louis H. Kauffman, Sostenes Lins. Read this book using Google Play Books app on your PC, android, iOS devices.

Download for offline reading, highlight, bookmark or take notes while you read Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM). This book contains the methods that are based on a recoupling theory for the Temperley-Lieb algebra. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant.

Temperley - Lieb Recoupling Theory and Invariants of 3-Manifolds Article in Classical and Quantum Gravity 13(12) August with 66 Reads How we measure 'reads'.

By Louis H. Kauffman and Sostenes L. Lins: pp., £, isbn 0 3 (Princeton University Press, ).Cited by: Get this from a library. Temperley-Lieb recoupling theory and invariants of 3-manifolds. [Louis H Kauffman; Sóstenes L Lins].

Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM) by Louis H. Kauffman () [Louis H. Kauffman;Sostenes Lins] on *FREE* shipping on qualifying offers.5/5(1). This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial.

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These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb Price: $ Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM), Volume Series: Book Book Series.

Frontmatter. Pages i-iv. Download PDF. Free Access; Contents. Pages v-x. Download PDF. Recognizing 3-Manifolds. Pages Get Access to Full Text.

Chapter Tables of Quantum Invariants. Pages Get Access to Full. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra.

This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world.

Abstract. This paper discusses combinatorial recoupling theory, first in relation to the vector cross product algebra and a reformulation of the Four Colour Theorem, and secondly in relation to the Temperley-Lieb algebra, the Jones polynomial and the SU(2) 3-Manifold invariants of Witten, Reshetikhin and by: 4.

This invaluable book is an introduction to knot and link invariants as generalised amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes a extraordinary range of interrelated topics in topology and mathematical physics.

The author takes a primarily combinatorial stance toward. On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory.

This paves the way for later discussion of the recently discovered Jones and generalized polynomials.5/5(2). Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM), Volume Louis H. Kauffman and Sostenes Lins This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial.

These are the .Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds, with Sostenes Lins, Princeton University Press, pp.Knots and Applications (Series on Knots and Everything, Vol 6)The Interface of Knots and Physics: American Mathematical Society Short Course January 2–3, San Francisco, California (Proceedings of Alma mater: Princeton University, Massachusetts.

Topological QuantumInformation Theory invariants of knots, links and threedimensional manifolds have been born of this interaction, and the form of the invariants is closely related to the form of the Temperley–Lieb recoupling Theory is based on the bracket polynomial model [37, 44] for the Jones polynomial.

It is built in terms. In the Temperley Lieb theory we obtainunitary(in fact real orthogonal) recoupling transformations when the bracket variable A has the form A = eiˇ=2r for r a positive integer. Thus we obtain families of unitary representations of the Artin braid group from the recoupling theory at these roots of unity.

Covariant loop quantum gravity, low energy perturbation theory, and Einstein gravity. arXiv Han, Temperley–Lieb Recoupling Theory and Invariants of 3-Manifolds.

Annals of Mathematics Studies, State sum invariants of 3 manifolds and quantum 6j Cited by:   The theory was made more systematic when quantum groups were invented, and is neatly summarised in chapters of the book of Kauffman and Lins, Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds.

It is a generalisation of the original spin networks due to. Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds Kauffman, Louis H.、Lins, Sostenes L. / Princeton Univ Pr / / $ (目前无人评价). Abstract. The attractor of a 3-manifold M 3 is the set of all 3-gems which have a minimum number of vertices and induce M 3.A gem (graph-encoded manifold) is a special edge graph which encodes a ball complex whose underlying space is a manifold.

Every 3-manifold is induced by a 3-gem. In this article I briefly recall the definitions and terminology of 3-gems, state some of the properties of Author: Sóstenes Lins. Temperley-Lieb recoupling theory and invariants of 3-manifolds Louis H.

Kauffman, Sostenes Lins Category: M_Mathematics, MD_Geometry and topology, MDat_Algebraic and differential topology. Temperley-Lieb recoupling theory and invariants of 3-manifolds. Princeton University Press. Louis H.

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Kauffman, Sostenes Lins. Temperley-Lieb recoupling theory and invariants of 3-manifolds. Princeton University Press. Louis H. Kauffman, A search query can be a title of the book, a name of the author, ISBN or anything else.

Louis H. Kauffman has 31 books on Goodreads with ratings. Louis H. Kauffman’s most popular book is Formal Knot Theory. Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM), Volume E-bok av Louis H Kauffman, Sostenes Lins E-bok, Engelska, Volume 4: Invariants of knots and 3-manifolds (Kyoto ) Pages – Problems on invariants of knots and 3-manifolds Edited by T.

Ohtsuki Abstract This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance. A skein theoretic proof of the Uq(g2)3-manifold invariant Temperley-Lieb recoupling theory and invariants of 3-manifolds.

is a modular Hopf algebra and hence produces invariants of 3. 3) Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds, by Louis Kauffman and Sostenes Lins, Annals of Mathematics Studies No. Princeton U. Press, pages, available July I described this briefly in "week17," before I had spent much time on it.

Let me recall the main point: in the late 80's Jones invented a new invariant. Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds Princeton University Press, [ISBN ] Kauffman, Stuart Investigations Oxford University Press, [ISBN X] Kauffman, Stuart A.

The Origins of Order: Self-Organization and Selection in Evolution Oxford University Press, [ISBN ]. Read Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM), Volume by Louis H. Kauffman, Sostenes Lins for free with a 30 day free trial.

Read unlimited* books and audiobooks on the web, iPad, iPhone and Android.He is the author of the books “Formal Knot Theory”, “On Knots”, “Temperley Lieb Recoupling Theory”, and “Invariants of 3-Manifolds” (Princeton University Press), and “Knots and Physics” (World Scientific Pub. Co.).

He has been a prominent leader in Knot Theory, one of the most active research areas in mathematics today.the author of the books “Formal Knot Theory”, “On Knots”, “Temperley Lieb Recoupling Theory and Invariants of 3-Manifolds” (Princ-eton University Press), and “Knots and Physics” (World Scientific Pub.

Co.). He has been a prominent leader in Knot Theory, one of the most active research areas in mathematics today.