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Untitled Prezi

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Mustafa Hajij

on 17 January 2015

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Transcript of Untitled Prezi

The colored Jones function
Example of the tail function
Why do we care?
Some properties of the tail of the colored Jones polynomial

Mustafa Hajij- Louisiana State University
The head and tail of the colored Jones polynomial
The extreme degrees of the colored Jones polynomial and link diagram
The extreme degrees of the colored Jones polynomial and link diagram
Another way to obtain the first N coefficients of the colored Jones polynomial of an alternating link from its diagram is the following (Armond, Dasbach) :
The head and tail of the colored Jones polynomial of alternating links only depends on the reduced checkerboard graphs of the knot diagrams.
The tail of the colored Jones polynomial depends on the reduced B graph
Product structure on the tail of the CJP
Theorem (Dasbach, Armond)
Product structure on the tail of the CJP
Theorem (H.)
The tail of a quantum spin networks
The products on reduced graphs are natural when one considers tails of
quantum spin networks with edges colored n, 2n
.
The Rogers-Ramanujan type identities, among other q-series identities, can also be proven naturally using quantum spin networks.
Giving explicit formulas for the q-series of alternating knots that were not possible with other techniques.
Thank You!
Example
Conference on Knot Theory and Its Applications to Physics and Quantum Computing

Jan 2015
Full transcript