Abstract
A new filtration of the spaces of tri-/univalent graphs [Formula: see text] that occur in the theory of finite-type invariants of knots and 3-manifolds is introduced. Combining the results of the two preceding articles, the quotients of this filtration are modeled by spaces of graphs with two types of edges and four types of vertices, and an upper bound for dim [Formula: see text] in terms of the dimensions of the filtration quotients is given. The degree m up to which [Formula: see text] is known is raised by two for u=0 and u=2.
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