AbstractIn this paper, we give lower bounds of the braid indices of surface-links by represented 4-charts by quandle cocycle invariants. As a consequence, we show that the braid index of the connected sum of a spun trefoil and a 2-twist spun trefoil is five, which is a special case of Tanakaʼs Problem
Knot theory has rapidly expanded in recent years. New representations of braid groups led to an extr...
Abstract. The triple point number of a surface-knot is defined to be the minimal number of triple po...
The goal of this paper is to determine the braid index of two types of complicated DNA polyhedral li...
AbstractIn this paper, we give lower bounds of the braid indices of surface-links by represented 4-c...
Abstract. The braid index of a surface-knot F is the minimum number among the degrees of all simple ...
The 2-twist spun trefoil is an example of a sphere that is knotted in 4-dimensional space. Here this...
AbstractState-sum invariants for knotted curves and surfaces using quandle cohomology were introduce...
The unknotting or triple point cancelling number of a surface link F is the least number of 1-handle...
AbstractThe unknotting or triple point cancelling number of a surface link F is the least number of ...
Abstract. The braid index of a surface-knot F is the minimum number among the degrees of all surface...
We consider surface links in the 4-space which can be deformed to simple branched coverings of a tri...
Abstract. We introduce a monoid corresponding to knotted surfaces in four space, from its hyperbolic...
We consider surface links in the 4-space which can be deformed to simple branched coverings of a tri...
A quandle is a set with a binary operation that satisfies three axioms that corresponds to the three...
Quandle cohomology theory was developed [6] to define invariants, called quandle cocycle (knot) inva...
Knot theory has rapidly expanded in recent years. New representations of braid groups led to an extr...
Abstract. The triple point number of a surface-knot is defined to be the minimal number of triple po...
The goal of this paper is to determine the braid index of two types of complicated DNA polyhedral li...
AbstractIn this paper, we give lower bounds of the braid indices of surface-links by represented 4-c...
Abstract. The braid index of a surface-knot F is the minimum number among the degrees of all simple ...
The 2-twist spun trefoil is an example of a sphere that is knotted in 4-dimensional space. Here this...
AbstractState-sum invariants for knotted curves and surfaces using quandle cohomology were introduce...
The unknotting or triple point cancelling number of a surface link F is the least number of 1-handle...
AbstractThe unknotting or triple point cancelling number of a surface link F is the least number of ...
Abstract. The braid index of a surface-knot F is the minimum number among the degrees of all surface...
We consider surface links in the 4-space which can be deformed to simple branched coverings of a tri...
Abstract. We introduce a monoid corresponding to knotted surfaces in four space, from its hyperbolic...
We consider surface links in the 4-space which can be deformed to simple branched coverings of a tri...
A quandle is a set with a binary operation that satisfies three axioms that corresponds to the three...
Quandle cohomology theory was developed [6] to define invariants, called quandle cocycle (knot) inva...
Knot theory has rapidly expanded in recent years. New representations of braid groups led to an extr...
Abstract. The triple point number of a surface-knot is defined to be the minimal number of triple po...
The goal of this paper is to determine the braid index of two types of complicated DNA polyhedral li...
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