Welcome to Yasutaka Nakanishi's Home Page

Produced by Yasutaka Nakanishi

Hello! Welcome to the home page of Yasutaka Nakanishi. Unfortunately, this page is under construction. Last update is December 2, 2008.


Research Interests by Keywords

Knot Theory: Alexander invariant, tangle, unknotting number, localized link theory (contained generalized unknotting operatuion), knot concordance, ribbon knot


Recent Works.

  1. Y. Nakanishi: Local moves and Gordian complexes, II, Kyungpook Mathematical Journal,, Vol. 47, No. 3 (September 2007), 329--334.

    Abstract: In this note, we will consider whether the knot sdpace is homogenious or not with respect to crossing-changes and Alexander matrices. pdf

  2. Y. Nakanishi and Y. Ohyama: Local moves and Gordian complexes, Journal of Knot Theory and Its Ramifications, Vol. 15, No. 9 (November 2006), 1215--1224.

    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

  3. Y. Nakanishi and Y. Ohyama: Knots with given finite type invariants and Conway polynomials, Journal of Knot Theory and Its Ramifications, Vol. 15, No. 2 (February 2006), 205--215.

  4. Y. Nakanishi, T. Shibuya, and A. Yasuhara: Self delta-equivalence of cobordant links, Proc. Amer. Math. Soc. 134, No. 8 (2006), 2465-2472.

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  5. Y. Nakanishi: A note on unknotting number, II, Journal of Knot Theory and Its Ramifications, Vol. 14, No. 1 (February 2005), 3--8.

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

  6. Y. Nakanishi and Y. Ohyama: Delta link homotopy for two component links, III, Journal of Mathematical Society of Japan, Vol. 55 no. 3 (2003, JULY), 641--654.

    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

  7. Y. Nakanishi and Y. Ohyama: Delta link homotopy for two component links, II, Journal of Knot Thory and Its Ramifications, Vol. 11 (2002), 353--362.

    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

  8. Y. Nakanishi and K. Nishizawa: On two dimensional knnots with reciprocal polynomials, Journal of Knot Thory and Its Ramifications, Vol. 10 no. 6 (2001), 841-850.

    Abstract: If a surface-knot has a projection with parallel-loop singularoties, then it has a reciprocal Alexander polynomial.

  9. Y. Nakanishi and M. Yamada: On Turk's Head Knots, Kobe J. Math. Vol. 17 no. 2 (2000), 119--130.

    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.

  10. Y. Nakanishi: Delta link homotopy for two component links, preprint (1999), to appear in Topology its Appl. (Proceedings of Mexico-Japan first joint meeting for Topology and its Appl.)

    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.

  11. Y. Nakanishi and T. Shibuya: Link homotopy and quasi self Delta-equivalence for links, Journal of Knot Theory and Its Ramifications Vol. 9 No. 5 (2000), 683-691.

    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.

  12. Y. Nakanishi and T. Shibuya: Relations among self Delta-equivalence and self Sharp-equivalences for links, in Series on Knots and Everything vol. 24: Knots in Hellas '98, Proceedings of the International Conference on Knot Theory and Its Ramifications, Editors: C. McA. Gordon, V. F. R. Jones, L. H. Kauffman, S. Lambropoulou, and J. H. Przytycki, World Sci. Publ., Singapore, 2000, 353-360.

    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.

  13. K. Nakamura, Y. Nakanishi, and Y. Uchida: Delta-unknotting number for knots, Journal of Knot Theory Its Ram., Vol.7 No.5 (1998), 639-650.

    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.

  14. Y. Nakanishi: Alexander invariant and twisting operation, KNOTS '96, Editor: S. Suzuki, World Sci. Publ., Singapore, 1997, pp. 327-335.

    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.


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