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We construct an infinite commutative lattice of groups whose dual spaces give Kauffman finite-type invariants of long virtual knots. The lattice is based "horizontally" upon the Polyak algebra and extended "vertically" using Manturov's functorial map f. For each n, the n-th vertical line in the lattice contains an infinite-dimensional subspace of Kauffman finite-type invariants of degree n. Moreover, the lattice contains infinitely many inequivalent extensions of the Conway polynomial to long virtual...
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