13 citations · 41 across the 14 of their papers we have counts for
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Surfaces in the 4-ball constructed using generators of knits and their graphical description
Inasa Nakamura, Jumpei Yasuda
We introduce a new construction of surfaces in , called knitted surfaces or BMW surfaces, which are described as the trace of deformations of knits. Here, knits are…
Torus-covering knot groups and their irreducible metabelian -representations
Inasa Nakamura
A torus-covering -knot is a surface-knot of genus one determined from a pair of commutative braids. For a torus-covering -knot , we determine the number of irreducible…
Branched covering surface-knots with degree three have the simplifying numbers less than three
Inasa Nakamura
A branched covering surface-knot is a surface-knot in the form of a branched covering over a surface-knot. For a branched covering surface-knot, we have a numerical invariant calle…
Simplifying branched covering surface-knots by chart moves involving black vertices
Inasa Nakamura
A branched covering surface-knot is a surface-knot in the form of a branched covering over an oriented surface-knot , where we include the case when the covering has no branch p…
Simplifying branched covering surface-knots by an addition of 1-handles with chart loops
Inasa Nakamura
A branched covering surface-knot over an oriented surface-knot is a surface-knot in the form of a branched covering over . A branched covering surface-knot over is prese…
Transformations of partial matchings
Inasa Nakamura
We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings.…
On addition of 1-handles with chart loops to 2-dimensional braids
Inasa Nakamura
A 2-dimensional braid over an oriented surface-knot is presented by a graph called a chart on a surface diagram of . We consider 2-dimensional braids obtained by an addition…
Showing distinctness of surface links by taking 2-dimensional braids
Inasa Nakamura
For an oriented surface link , we can take a satellite construction called a 2-dimensional braid over , which is a surface link in the form of a covering over . We demonst…
Satellites of an oriented surface link and their local moves
Inasa Nakamura
For an oriented surface link in , we consider a satellite construction of a surface link, called a 2-dimensional braid over , which is in the form of a coverin…
On surface links whose link groups are abelian
Tetsuya Ito, Inasa Nakamura
We study surface links whose link groups are free abelian, and construct various stimulating and highly non-trivial examples of such surface links.
Unknotting numbers and triple point cancelling numbers of torus-covering knots
Inasa Nakamura
It is known that any surface knot can be transformed to an unknotted surface knot or a surface knot which has a diagram with no triple points by a finite number of 1-handle additio…
Triple linking numbers and triple point numbers of certain -links
Inasa Nakamura
The triple linking number of an oriented surface link was defined as an analogical notion of the linking number of a classical link. We consider a certain -component -link…
Surface links with free abelian link groups
Inasa Nakamura
It is known that if a classical link group is a free abelian group, then its rank is at most two. It is also known that a -component 2-link group () is not free abelian. In…
Unknotting surface links which are coverings of a trivial torus knot
Inasa Nakamura
We consider surface links in the 4-space which are presented by the form of simple branched coverings over the standard torus, which we call torus-covering links. In this paper, we…
Braiding surface links which are coverings over the standard torus
Inasa Nakamura
We consider a surface link in the 4-space which can be presented by a simple branched covering over the standard torus, which we call a torus-covering link. Torus-covering links in…
Surface links which are coverings over the standard torus
Inasa Nakamura
We introduce a new construction of a surface link in the 4-space. We construct a surface link as a branched covering over the standard torus, which we call a torus-covering link. W…