Applying Lipson's state models to marked graph diagrams of surface-links

Abstract

A. S. Lipson constructed two state models yielding the same classical link invariant obtained from the Kauffman polynomial F (a, z). In this paper, we apply Lipson's state models to marked graph diagrams of surface-links, and observe when they induce surface-link invariants.Mathematics Subject Classification 2000: 57Q45; 57M25.

Polynomial of an oriented surface-link diagram via quantum A2 invariant

“…See Section 2 for details. By using marked graph diagrams, some properties and invariants of surface-links were studied in [1,3,4,6,9,10,13,14,15,16,19,21].…”

Constructions of invariants for surface-links via link invariants and applications to the Kauffman bracket

“…By a surface-link (or knotted surface) we mean a closed 2-manifold smoothly (or piecewise linearly and locally flatly) embedded in the 4-space R 4 or S 4 . Two surfacelinks are said to be equivalent if they are ambient isotopic.…”

“…Using marked graph diagram presentations of surfacelinks, some properties and invariants for surface-links have been studied by several researchers up to now. For example, see [1,4,5,7,13,14,17,18,19,23,25] and therein.…”

On generating sets of Yoshikawa moves for marked graph diagrams of surface-links

“…Using these terminologies, some properties and invariants of surface-links were studied in [2,5,6,12,13,14,15,22,25]. On many occasions it is necessary to minimize the number of Yoshikawa moves on marked graph diagrams when one checks that a certain function from marked graph diagrams defines a surface-link invariant.…”