23 citations · 52 across the 17 of their papers we have counts for
18 papers
Parallelization of Welded Links
Naoko Kamada, Seiichi Kamada
The notion of a welded link was introduced by Fenn, Rimányi, and Rourke as an analogue of welded braids. A welded link is defined as an equivalence class of link diagrams that may…
Invariants of virtual links and twisted links using affine indices
Naoko Kamada, Seiichi Kamada
The affine index polynomial and the -writhe are invariants of virtual knots which are introduced by Kauffman and by Satoh and Taniguchi independently. They are defined by using…
Diagrams realizing prescribed sublink diagrams for virtual links and welded links
Naoko Kamada
Jin and Lee proved the following: Suppose that are link diagrams. Given a link which is partitioned into sublinks admitting diagrams $D_1, \…
Doodles and commutator identities
Andrew Bartholomew, Roger Fenn, Naoko Kamada +1
A doodle is a collection of immersed circles without triple intersections in the -sphere. It was shown by the second author and P.~Tayler that doodles induce commutator identiti…
Cyclic coverings of virtual link diagrams
Naoko Kamada
A virtual link diagram is called mod almost classical if it admits an Alexander numbering valued in integers modulo , and a virtual link is called mod almost classical i…
Colorings and doubled colorings of virtual doodles
Andrew Bartholomew, Roger Fenn, Naoko Kamada +1
A virtual doodle is an equivalence class of virtual diagrams under an equivalence relation generated by flat version of classical Reidemesiter moves and virtual Reidemsiter moves s…
On Gauss codes of virtual doodles
Andrew Bartholomew, Roger Fenn, Naoko Kamada +1
We discuss Gauss codes of virtual diagrams and virtual doodles. The notion of a left canonical Gauss code is introduced and it is shown that oriented virtual doodles are uniquely p…
Virtual links which are equivalent as twisted links
Naoko Kamada, Seiichi Kamada
A virtual link is a generalization of a classical link that is defined as an equivalence class of certain diagrams, called virtual link diagrams. It is further generalized to a twi…
Coherent double coverings of virtual link diagrams
Naoko Kamada
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representati…
Doodles on surfaces
Andrew Bartholomew, Roger Fenn, Naoko Kamada +1
Doodles were introduced in [R. Fenn and P. Taylor, Introducing doodles, Topology of low-dimensional manifolds, pp. 37--43, Lecture Notes in Math., 722, Springer, Berlin, 1979] but…
Converting virtual link diagrams to normal ones
Naoko Kamada
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representati…
A twisted link invariant derived from a virtual link invariant
Naoko Kamada
Virtual knot theory is a generalization of knot theory which is based on Gauss chord diagrams and link diagrams on closed oriented surfaces. A twisted knot is a generalization of a…
Double coverings of twisted links
Naoko Kamada, Seiichi Kamada
Twisted links are a generalization of virtual links. As virtual links correspond to abstract links on orientable surfaces, twisted links correspond to abstract links on (possibly n…
Surface pole bracket polynomials of virtual knots and twisted knots
Naoko Kamada
Dye and Kauffman defined surface bracket polynomials for virtual links by use of surface states, and found a relationship between the surface states and the minimal genus of a surf…
Biquandles with structures related to virtual links and twisted links
Naoko Kamada, Seiichi Kamada
We introduce two kinds of structures, called v-structures and t-structures, on biquandles. These structures are used for colorings of diagrams of virtual links and twisted links su…
New Invariants of Long Virtual Knots
Andrew Bartholomew, Roger Fenn, Naoko Kamada +1
This paper extends the construction of invariants for virtual knots to virtual long knots and introduces two new invariant modules of virtual long knots. Several interesting featur…
Span of the Jones polynomial of an alternating virtual link
Naoko Kamada
For an oriented virtual link, L.H. Kauffman defined the f-polynomial (Jones polynomial). The supporting genus of a virtual link diagram is the minimal genus of a surface in which t…
On the Jones polynomials of checkerboard colorable virtual knots
Naoko Kamada
The notion of chckerboard colorability for virtual links and abstract links is introduced. We study the Jones polynomials of virtual links and abstruct links. It is proved that a c…