# YOSHIAKI UCHIDA

### (Recent) Preprints and prints:

1. Detecting inequivalence of some unknotting tunnels for two-bridge knots
Proc. of KAIST Math. Workshop, 5 (1990) 227-232
2. Non-simple links with tunnel number one. with M. Eudave-Munoz
Proc. of A.M.S., 124 (1996) 1567-1575

We determine all non-simple links which admit an unknotting tunnel, i.e. links which contain an essential annulus or torus in its exterior and have tunnel number one.

3. Motions of trivial links, and ribbon knots. with Y.Marumoto, T. Yasuda.
Michigan Math. J. 42 (1995) 463-477

A motion of a link consists of an isotopy of the link through its ambient space that ultimately returns the link to itself. Using the result on motions of a trivial link, we can define an invariant of ribbon presentaions of knots.

4. Delta-unknotting number for knots. with K.Nakamura, Y.Nakanishi
Journal of Knot theory and Its Ramifications, Vol. 7 (1998) 630-650

We determine $\Delta$-unknotting for torus knots, positive knots, and positive closed 3-braid.

5. Two-bridge knots with generalized unknotting number one,
Proc. of Knots 96 ed. S. Suzuki pp.109-113 (1996)

We define $b/a$-unknotting operation as a generalized unknotting operation. And we determine all two-bridge knots with $b/a$-unknotting number one. For an ordinary unknotting operation, Kanenobu and Murakami determined all unknotting number one two-bridge knots. And P. Kohn determined all unknotting number one two-bridge links.

6. Periodic knots with unknotting number one,
Knots in Hellas '98 Series on Knots and Everything Vol.24 pp. 524--529 (2000)

We show that for many periodic knots its $\Delta$-unknotiing number is greater than one.

7. The Gordian complex of knots, with M.Hirasawa
Jour. Knot Theory Ramifications, Vol. 11, No. 3 (2002) 363-368.

We define the Gordian complex of the space
of oriented knot types, and announce the following: Let $K_0$ and $K_1$ be
any pair of knot types such that the Gordian distance $d_G(K_0;K_1) = 1$.
Then there exists a family of knot types $\{K_0, K_1, K_2, \ldots, K_n\}$  such that
$d_G(K_i;K_j ) = 1$ for any $i < j$.

pdf file by M.Hirasawa.

8. Double torus knots, tunnel number one knots, and essential disks

Let $W$ be a genus two handlebody, $D$ is essential, if $D$ is properly embedded disk in $W$ and not $\partial$-pararell in $W$. Cutting $W$ along $D$, then we get a solid torus or two solid tori. In case of a solid torus, its core is a tunnel number one knot, in case of two solid tori, its core is a tunnel number one links. From this view, we will characteristic some tunnel number one knot.

ps file

9. On three-fold irregular branched covering over closed three-braid and three-bridge knots

Proceedings of International Conference on Topology in Matsue,Topology and its Applications 146-147 (2005) 189-194

10. The detour crossing changes
Kobe J. Math. 31 (2014) 1-7
11. Delta-unknotting operations and ordinary unknotting operations
Y. Uchida
The Proceedings of International
Conference on Topology and Geometry 2013, joint with the 6th
Japan-Mexico Topology Symposium
Topology and its Applications (to appear)
12. Characterization of Supramolecular Hidden Chirality of Hydrogen-Bonded Networks by Advanced Graph Set Analysis

Toshiyuki Sasaki, Yoko Ida1, Dr. Ichiro Hisaki, Dr. Tetsuharu Yuge, Prof. Dr. Yoshiaki Uchida,
Dr. Norimitsu Tohnai and Prof. Dr. Mikiji Miyata

Chemistry - A European Journal
Volume 20, Issue 9, pages 2478-2487, February 24, 2014