  We generalize the braid algebra to the case of loops with intersections. We
introduce the Reidemeister moves for 4 and 6-valent vertices to have a theory
of rigid vertex equivalence. By considering representations of the extended
braid algebra, we derive skein relations for link polynomials, which allow us
to generalize any link Polynomial to the intersecting case. We perturbatively
show that the HOMFLY Polynomials for intersecting links correspond to the
vacuum expectation value of the Wilson line operator of the Chern Simon's
Theory. We make contact with quantum gravity by showing that these polynomials
are simply related with some solutions of the complete set of constraints with
cosmological constant
