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A lattice of finite-type invariants of virtual knots

Volume 100 / 2014

Micah W. Chrisman Banach Center Publications 100 (2014), 27-49 MSC: 57M25,57M27. DOI: 10.4064/bc100-0-2


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 knots, all of which satisfy the same skein relation. Bounds for the rank of each group in the lattice are obtained.


  • Micah W. ChrismanDepartment of Mathematics
    Monmouth University
    West Long Branch, NJ 07764, USA

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