A lattice of finite-type invariants of virtual knots

• Autorzy: Micah W. Chrisman
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57M27: Invariants of knots and 3-manifolds
• 57M25: Knots and links in S 3

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2014
• Tom: 100
• Numer: 1
• Strony: 27-49

Daty

wydano

2014

Twórcy

autor

Micah W. Chrisman

• Department of Mathematics, Monmouth University, West Long Branch, NJ 07764, USA

Identyfikatory

DOI

10.4064/bc100-0-2