3 citations · 6 across the 7 of their papers we have counts for
10 papers
On biquandles for the groups and surface singular braid monoid
Sang Youl Lee, Vassily Olegovich Manturov, Igor Mikhailovich Nikonov
The groups were defined by V. O. Manturov in order to describe dynamical systems in configuration systems. In the paper we consider two applications of this theory: we defi…
Biquandle cohomology and state-sum invariants of links and surface-links
Seiichi Kamada, Akio Kawauchi, Jieon Kim +1
In this paper, we discuss the (co)homology theory of biquandles, derived biquandle cocycle invariants for oriented surface-links using broken surface diagrams and how to compute th…
Presentation of immersed surface-links by marked graph diagrams
Seiichi Kamada, Akio Kawauchi, Jieon Kim +1
It is well known that surface-links in 4-space can be presented by diagrams on the plane of 4-valent spatial graphs with makers on the vertices, called marked graph diagrams. In th…
Constructions of invariants for surface-links via link invariants and applications to the Kauffman bracket
Sang Youl Lee
In this paper, we formulate a construction of ideal coset invariants for surface-links in -space using invariants for knots and links in -space. We apply the construction to…
Polynomial of an oriented surface-link diagram via quantum A_2 invariant
Yewon Joung, Seiichi Kamada, Akio Kawauchi +1
It is known that every surface-link can be presented by a marked graph diagram, and such a diagram presentation is unique up to moves called Yoshikawa moves. G. Kuperberg introduce…
Computations of quandle cocyle invariants of surface-links using marked graph diagrams
Seiichi Kamada, Jieon Kim, Sang Youl Lee
By using the cohomology theory of quandles, quandle cocycle invariants and shadow quandle cocycle invariants are defined for oriented links and surface-links via broken surface dia…
On generating sets of Yoshikawa moves for marked graph diagrams of surface-links
Jieon Kim, Yewon Joung, Sang Youl Lee
A marked graph diagram is a link diagram possibly with marked -valent vertices. S. J. Lomonaco, Jr. and K. Yoshikawa introduced a method of representing surface-links by marked…
Applying Lipson's state models to marked graph diagrams of surface-links
Yewon Joung, Seiichi Kamada, Sang Youl Lee
A. S. Lipson constructed two state models yielding the same classical link invariant obtained from the Kauffman polynomial . In this paper, we apply Lipson's state models t…
Crossing number of an alternating knot and canonical genus of its Whitehead double
Hee Jeong Jang, Sang Youl Lee
A conjecture proposed by J. Tripp in 2002 states that the crossing number of any knot coincides with the canonical genus of its Whitehead double. In the meantime, it has been estab…
The canonical genus for Whitehead doubles of a family of alternating knots
Hee Jeong Jang, Sang Youl Lee
For any given integer and a quasitoric braid with , we prove that the maximum degree in of the HOMFLYPT…