Download E-books Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134) PDF

By Louis H. Kauffman

This ebook deals a self-contained account of the 3-manifold invariants bobbing up from the unique Jones polynomial. those are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. ranging from the Kauffman bracket version for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of hyperlinks are developed and mixed to shape the 3-manifold invariants. The tools during this ebook are according to a recoupling thought for the Temperley-Lieb algebra. This recoupling thought is a q-deformation of the SU(2) spin networks of Roger Penrose.

The recoupling concept is built in a only combinatorial and easy demeanour. Calculations are in keeping with a reformulation of the Kirillov-Reshetikhin shadow international, resulting in expressions for the entire invariants by way of country summations on 2-cell complexes. huge tables of the invariants are incorporated. Manifolds in those tables are well-known via surgical procedure displays and by way of 3-gems (graph encoded 3-manifolds) in an process pioneered by way of Sostenes Lins. The appendices contain information regarding gem stones, examples of precise manifolds with an identical invariants, and purposes to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.

Show description

Read Online or Download Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134) PDF

Similar Combinatorics books

Difference Equations, Second Edition: An Introduction with Applications

Distinction Equations, moment version, offers a pragmatic advent to this crucial box of suggestions for engineering and the actual sciences. subject insurance comprises numerical research, numerical tools, differential equations, combinatorics and discrete modeling. a trademark of this revision is the various program to many subfields of arithmetic.

Finite Projective Spaces of Three Dimensions (Oxford Mathematical Monographs)

This self-contained and hugely distinctive research considers projective areas of 3 dimensions over a finite box. it's the moment and center quantity of a three-volume treatise on finite projective areas, the 1st quantity being Projective Geometrics Over Finite Fields (OUP, 1979). the current paintings restricts itself to 3 dimensions, and considers either subject matters that are analogous of geometry over the advanced numbers and themes that come up out of the fashionable conception of prevalence buildings.

Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry

A gradual creation to the hugely subtle global of discrete arithmetic, Mathematical difficulties and Proofs offers themes starting from easy definitions and theorems to complicated themes -- akin to cardinal numbers, producing services, houses of Fibonacci numbers, and Euclidean set of rules.

Intuitive Combinatorial Topology (Universitext)

Topology is a comparatively younger and extremely vital department of arithmetic, which reports the houses of items which are preserved via deformations, twistings, and stretchings. This ebook offers with the topology of curves and surfaces in addition to with the elemental recommendations of homotopy and homology, and does this in a full of life and well-motivated means.

Extra resources for Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134)

Show sample text content

Rated 4.15 of 5 – based on 24 votes