$G_{n}^{3}$ group and graph-valued invariant
Abstract
In this talk we introduce a modification of the $G_{n}^{3}$ group and construct a map from the braid group to framed 6-valent graphs with leaves using this modified group. By extending this idea we construct a knot invariant valued in equivalence classes of graphs up to local moves by using the plat closure of braids.
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