Yasutaka Nakanishi

Delta link homotopy for two component links

Abstract In this note, we will study Δ link homotopy (or self Δ -equivalence), which is an equivalence relation of ordered and oriented link types. We will give a necessary condition in the terms of Conway polynomials for two link types to be Δ link homotopic. As an application, we will classify (ordered and oriented) prime two-component link types with seven crossings or less up to Δ link homotopy.

LINK HOMOTOPY AND QUASI SELF DELTA-EQUIVALENCE FOR LINKS

In this note, we will study on equivalence relations for links and we will give a necessary condition for equivalence in terms of the Alexander polynomial and show their differences.

Self delta-equivalence of cobordant links

Self A-equivalence is an equivalence relation for links, which is stronger than the link-homotopy defined by J. Milnor. It is known that cobordant links are link-homotopic and that they are not necessarily self A-equivalent. In this paper, we will give a sufficient condition for cobordant links to be self A-equivalent.

DELTA-UNKNOTTING NUMBER FOR KNOTS

The Δ-unknotting number for a knot is defined to be the minimum number of Δ-unknotting operations which deform the knot into the trivial knot. We determine the Δ-unknotting numbers for torus knots, positive pretzel knots, and positive closed 3-braids.

On effective 9-colorings for knots

For a 1- or 2-dimensional knot, we give a lower bound log2 n + 1 of the minimum number of distinct colors for all effective n-colorings. In particular, we prove that any effectively 9-colorable 1- or ribbon 2-knot is presented by a diagram where exactly five colors of nine are assigned to the arcs or sheets.

RELATIONS AMONG SELF DELTA-EQUIVALENCE AND SELF SHARP-EQUIVALENCES FOR LINKS

In this note, we will study on generalized unknotting operations for links, especially with the condition to restrict their deformations for the same component, and we will show their differences.

A NOTE ON UNKNOTTING NUMBER, II

In this note, we will give an approach to determine the unknotting number by a surgical view of Alexander matrix.

ON GENERALIZED UNKNOTTING OPERATIONS

If a set of local moves can transform every knot into a trivial knot, it is called a generalized unknotting operation. The author collects generalized unknotting operations and classify them up to local equivalence.

Alexander polynomials of two-bridge knots

For two-bridge knots, the authors give necessary conditions on coefficients of Alexander polynomials.

11-Colored knot diagram with five colors

We prove that any