Hello! Welcome to the home page of Yasutaka Nakanishi. Unfortunately, this page is under construction. Last update is December 2, 2008.
Abstract: In this note, we will consider whether the knot sdpace is homogenious or not with respect to crossing-changes and Alexander matrices. pdf
Abstract: In this note, we will consider whether the knot sdpace is homogenious or not with respect to $C_n$ moves and Conway polynomials. pdf
Abstract: In this note, we will give an approach to determine the unknotting number by a surgical view of Alexander matrix. ps, pdf
Abstract: Delta link homotopy is an equivalence relation generated by self Delta-move. A pair of integral invariants is a faithful invariant for ordered, oriented, and prime 2-components link types up to Delta link homotopy. ps
Abstract: Delta link homotopy is an equivalence relation generated by self Delta-move. A pair of integral invariants classifies all ordered, oriented, and prime 2-components link types. We will study the possible values of the invariants. ps.gz
Abstract: If a surface-knot has a projection with parallel-loop singularoties, then it has a reciprocal Alexander polynomial.
Abstract: The $\Delta$-unknotting number for a knot is defined to be the minimum number of $\Delta$-unknotting operation which deform the knot into a trivial knot. We determine the $\Delta$-unknotting number for a sub-family of Turk's head knots.
Abstract: Delta link homotopy is an equivalence relation generated by self Delta-move. In this note, we will classify all ordered and oriented prime 2-component links with 7 crossing or less.
Abstract: We will study on generalized unknotting operations for links, especially with the condition to restrict their defoemations for the same components, and we will show their defferences.
Abstract: We will study on generalized unknotting operations for links, especially with the condition to restrict their defoemations for the same components, and we will show their defferences.
Abstract: The $\Delta$-unknotting number for a knot is defined to be the minimum number of $\Delta$-unknotting operation which deform the knot into a trivial knot. We determine the $\Delta$-unknotting number for torus knots, positive pretzel knots, and positive closed $3$-braids.
Abstract: The Borromean rings and the $3$-component trivial link cannot be deformed to each other by a finite sequence of link-homotopies and cancellations of $4$-consecutive crossings.