A diagrammatic approach to the AJ conjecture (joint with Stavros Garoufalidis)

(joint w/ Stavros Garoufalidis)    

 

The colored Jones polynomials J_n(K) of a knot K are known to satisfy some recurrence relations,
which are described by a non commutative two variable polynomial Â(q,L,M). The AJ conjecture states that
the specialization Â(q=1,L,M) is equal to the A-polynomial of K, whose zero set is the SL_2 character variety
of K.Using the theory of certificates, we prove a weak form of the AJ conjecture:
For any knot K, Â(q=1,L,M) divides a power of the A-polynomial.