Temperleylieb recoupling theory and invariants of 3manifolds am4 ebook written by louis h. L kauffman, s lins, temperleylieb recoupling theory and invariants of 3manifolds, annals of maths studies 4, princeton university press 1994 a a kirillov, geometric quantization, from. Foundations of the colored jones polynomial of singular knots. Starting from the kauffman bracket model for the jones polynomial and the diagrammatic temperleylieb. Temperleylieb recoupling theory and invariants of 3. Temperleylieb recoupling theory and invariants of 3manifolds am4, volume 4 louis h. Lins, temperley lieb recoupling theory and invariants of 3manifolds, annals. Quantum invariants of knots and 3 manifolds pdf bulletin new series of the. Priinceton annals of mathematics studies print isbn ebook. On the tqft representations of the mapping class groups.
The temperley lieb algebra can be extended to the algebra t n of. Threedimensional link theory and invariants of plane curve singularities. Saintaubin, standard modules, induction and the structure of the temperleylieb algebra, adv. Pdf a generalization of the gram determinant of type a. Temperley lieb algebra ii uwe kaiser boise state university.
Lins, temperleylieb recoupling theory and invariants of 3manifolds, annals. D3, we can either produce a theory by relating a heegaard splitting or more. This book contains the methods that are based on a recoupling theory for the temperleylieb algebra. Offers an account of the 3manifold invariants arising from the original jones polynomial. Kauffman, 9780691036403, available at book depository with free delivery worldwide. The department of mathematics of the university of south. This invaluable book is an introduction to knot and link invariants as generalised amplitudes for a quasiphysical process. On the classicality of brodas su2 invariants of 4manifolds louis crane1 department of mathematics kansas state university manhattan, ks 665062602 louis h.
Kishinos knot is not detected by the fundamental group or the bracket polynomial. Temperleylieb recoupling theory and invariants of 3manifolds am4, volume 4 by louis h. This book is an introductory explication on the theme of knot and link invariants as generalized amplitudes vacuumvacuum amplitudes for a quasiphysical process. The ideas outlined above lead not only to numerical invariants of 3manifolds but rather to a. Temperleylieb recoupling theory and invariants of 3manifolds, ann. Framization of the temperleylieb algebra and related link invariants phd thesis. Buy temperleylieb recoupling theory and invariants of 3manifolds am4 on free shipping on qualified orders. New invariants in the theory of knots pdf file of paper by lk in the american mathematical monthly 1987. Homflypt regular isotopy pdf file of notes by lk in which the twovariable homflypt polynomial is proved to be an invariant via the use of induction on diagrams, reidemeister moves and regular isotopy. He is known for the introduction and development of the bracket polynomial and the kauffman polynomial. Temperley lieb recoupling theory and invariants of 3manifolds article in classical and quantum gravity 12 august 2009 with 64 reads how we measure reads. We provide a protocol to physically generate a 2qutrit entangling gate in the kauffmanjones version of s u 2 chernsimons theory at level 4. This book offers a selfcontained account of the 3manifold invariants arising from the original jones polynomial. Asymptotic expansions of wittenreshetikhinturaev invariants for.
One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the 20th century. Temperley lieb recoupling theory and invariants of 3. 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 temperleylieb algebra, the jones polynomial and the su2 3manifold invariants of witten, reshetikhin and turaev. Temperleylieb recoupling theory and invariants of 3manifolds.
Temperleylieb recoupling theory and invariants of 3manifolds am4 kauffman, louis h lins, so 9780691036403 9781400882533. Louis hirsch kauffman born february 3, 1945 is an american mathematician, topologist, and professor of mathematics in the department of mathematics, statistics, and computer science at the university of illinois at chicago. B2 invariants derived from the recoupling theory of the temperleylieb. The invariants obtained for closed 3manifolds are almost the same, but their tqft extensions are. Lins, temperleylieb recoupling theory and invariants of 3manifolds princeton university press, princeton, 1994. Protocol for making a 2qutrit entangling gate in the.
He has been a prominent leader in knot theory, one of the most active research areas in mathematics today. These are the wittenreshetikhinturaev and the turaevviro invariants. The protocol uses elementary operations on anyons consisting of braids, interferometric measurements. Princeton university press is proud to have published the annals of mathematics studies since 1940. This is a recoupling theory that generalizes standard angular momentum recoupling theory, generalizes the penrose the ory of spin networks and is inherently topological. The data for the construction of the invariant is a tensor category with a condition on the duals, which we have called a spherical category. We develop a skein recoupling theory for quantum g 2 involving skeins of 1 or 2 strands. Threemanifolds and the temperleylieb algebra springerlink. Temperley lieb recoupling theory and invariants of 3manifolds, princeton university press, annals studies 114, 1994. On the classicality of brodas su2 invariants of 4manifolds. Back to temperleylieb recoupling theory and invariants of 3manifolds am4, volume 4 find in a library find temperleylieb recoupling theory and invariants of 3manifolds am4, volume 4 near you.
Buy temperleylieb recoupling theory and invariants of 3manifolds am4 on. The recoupling theory is used to define a combinatorial method for computing quantum g 2 3manifold invariants at 15th and 18th roots of unity. Temperleylieb recoupling theory is based on the bracket polynomial model 37, 44 for the jones polynomial. By now several approachs are available for constructing the. The demands of knot theory, coupled with a quantumstatistical framework, create a context that naturally and powerfully includes a extraordinary range of interrelated topics in topology and mathematical physics. In what follows, we use temperleylieb recoupling theory cf. Dipartimento di fisica, universit degli studi di parma and infn, gruppo collegato di parma, 43100 parma, italy i discuss the role played by the spinnetwork basis and recoupling theory in its graphical tangle. The demands of the knot theory, coupled with a quantum statistical frame work create a context that naturally and powerfully includes an extraordinary range of interelated topics in topology and mathematical. This article is an introduction to relationships between knot theory and theoretical physics. Download for offline reading, highlight, bookmark or take notes while you read temperleylieb recoupling theory and invariants of 3manifolds am4. Part iii provides constructions of modular categories, based on. However, we can show that kishinos knot is not equivalent to unknot by applying either the 3strand bracket polynomial or the surface bracket polynomial. The methods in this book are based on a recoupling theory for the temperleylieb algebra. View enhanced pdf access article on wiley online library html view download pdf for offline viewing.
Dynamical systems iv, encyclopaedia of mathematical sciences 4 v i arnold and s p novikov, editors springer 1990. Temperleylieb recoupling theory and invariants of 3manifolds am4 by louis h. Combinatorial recoupling theory and 3manifold invariants. Starting from the kauffman bracket model for the jones polynomial and the diagrammatic temperleylieb algebra, higherorder polynomial invariants of links are constructed and combined to form the 3manifold invariants. This recoupling theory is a qdeformation of the su2 spin networks of roger penrose. In this paper, we construct two nontrivial virtual knot diagrams, k. The construction is in the spirit of topological quantum eld theory and the invariant is calculated from a triangulation of the 3manifold. This gives a vast class of knot invariants and 3manifold invariants as well as a class of linear. M,l, of embeddings of links l in 3manifolds m, known.
Lins, sostenes temperleylieb recoupling theory and invariants of 3manifolds am4, volume 4. The kauffman bracket skein module of the 3manifold m is the. Spiders for rank 2 lie algebras springer for research. The grothendieck group of a tower of the temperleylieb. We give an exposition of the theory of polynomial invariants of knots and links, the witten functional integral formulation of knot and link invariants, and the beginnings of topological quantum field theory, and show how the theory of knots is related to a number of key issues in mathematical. Spin networks and recoupling in loop quantum gravity.
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