Homotopy, Delta-equivalence and concordance for knots in the complement of a trivial link (2009)
Fleming, Thomas, Shibuya, Tetsuo, Tsukamoto, Tatsuya, Yasuhara, Akira
Link-homotopy and self Delta-equivalence are equivalence relations on links. It was shown by J. Milnor (resp. the last author) that Milnor invariants determine whether or not a link is link-homotopic...
Characterization of Finite Type String Link Invariants of Degree < 5 (2009)
Meilhan, Jean-Baptiste, Yasuhara, Akira
In this paper, we give a complete set of finite type string link invariants of degree
Regular homotopic deformation of compact surface with boundary and mapping class group (2009)
Hirose, Susumu, Yasuhara, Akira
A necessary and sufficient algebraic condition for a diffeomorphism over a surface embedded in the 3-sphere to be induced by a regular homotopic deformation is discussed, and a formula for the number...
Characterization of finite type string link invariants of degree < 5 (2009)
Meilhan, Jean-Baptiste, Yasuhara, Akira
In this paper, we give a complete set of finite type string link invariants of degree
Characterization of finite type string link invariants of degree < 5 (2009)
Meilhan, Jean-Baptiste, Yasuhara, Akira
In this paper, we give a complete set of finite type string link invariants of degree
Whitehead double and Milnor invariants (2007)
Meilhan, Jean-Baptiste, Yasuhara, Akira
We consider the operation of Whitehead double on a component of a link and study the behavior of Milnor invariants under this operation. We show that this operation turns a link whose Milnor...
Self delta-equivalence for links whose Milnor's isotopy invariants vanish (2006)
For an $n$-component link $L$, the Milnor's isotopy invariant is defined for each multi-index $I=i_1i_2...i_m (i_j\in\n)$. Here $m$ is called the length. Let $r(I)$ denote the maximam number of times...
Meilhan, Jean-Baptiste, Yasuhara, Akira
A C_n-move is a local move on links defined by Habiro and Goussarov, which can be regarded as a `higher order crossing change'. We use Milnor invariants with repeating indices to provide several...
Milnor's Isotopy Invariants and Generalized Link Homotopy (2005)
Fleming, Thomas, Yasuhara, Akira
It has long been known that a Milnor invariant with no repeated index is an invariant of link homotopy. We show that Milnor's invariants with repeated indices are invariants not only of isotopy, but...
Brunnian local moves of knots and Vassiliev invariants (2004)
K. Habiro gave a neccesary and sufficient condition for knots to have the same Vassiliev invariants in terms of $C_k$-move. In this paper we give another geometric condition in terms of Brunnian...
Classification of $n$-component Brunnian links up to $C_n$-move (2004)
Miyazawa, Haruko Aida, Yasuhara, Akira
We give a classification of $n$-component links up to $C_n$-move. In order to prove this classification, we characterize Brunnian links, and have that a Brunnian link is ambient isotopic to a band...
Dabkowski, Mieczyslaw K., Ishiwata, Makiko, Przytycki, Jozef H., Yasuhara, Akira
Rotors were introduced in Graph Theory by W.Tutte. The concept was adapted to Knot Theory as a generalization of mutation by Anstee, Przytycki and Rolfsen in 1987. In this paper we show that...
A factorization of the Conway polynomial and covering linkage invariants (2004)
Tsukamoto, Tatsuya, Yasuhara, Akira
J.P. Levine showed that the Conway polynomial of a link is a product of two factors: one is the Conway polynomial of a knot which is obtained from the link by banding together the components; and the...
Przytycki, Jozef H., Yasuhara, Akira
We study the linking numbers in a rational homology 3-sphere and in the infinite cyclic cover of the complement of a knot. They take values in $\Bbb Q$ and in ${Q}({\Bbb Z}[t,t^{-1}])$ respectively,...
Branched covers of tangles in three-balls (2001)
Ishiwata, Makiko, Przytycki, Józef H., Yasuhara, Akira
We give an algorithm for a surgery description of a $p$-fold cyclic branched cover of $B^3$ branched along a tangle. We generalize constructions of Montesinos and Akbulut-Kirby.
Local moves on spatial graphs and finite type invariants (2001)
Taniyama, Kouki, Yasuhara, Akira
We define $A_k$-moves for embeddings of a finite graph into the 3-sphere for each natural number $k$. Let $A_k$-equivalence denote an equivalence relation generated by $A_k$-moves and ambient...
$C_k$-moves on spatial theta-curves and Vassiliev invariants (2001)
The $C_k$-equivalence is an equivalence relation generated by $C_k$-moves defined by Habiro. Habiro showed that the set of $C_k$-equivalence classes of the knots forms an abelian group under the...
Torus knots that cannot be untied by twisting (2001)
Nouh, Mohamed Ait, Yasuhara, Akira
We give a necessary condition for a torus knot to be untied by a single twisting. By using this result, we give infinitely many torus knots that cannot be untied by a single twisting.
Symmetry of links and classification of lens spaces (2000)
Przytycki, Jozef H., Yasuhara, Akira
We give a concise proof of a classification of lens spaces up to orientation-preserving homeomorphisms. The chief ingredient in our proof is a study of the Alexander polynomial of ` symmetric' links...
Classification of links up to self $#$-move (2000)
Shibuya, Tetsuo, Yasuhara, Akira
A pass-move and a $#$-move are local moves on oriented links defined by L.H. Kauffman and H. Murakami respectively. Two links are self pass-equivalent (resp. self $#$-equivalent) if one can be...
Band description of knots and Vassiliev invariants (2000)
Taniyama, Kouki, Yasuhara, Akira
In 1993 K. Habiro defined $C_k$-move of oriented links and around 1994 he proved that two oriented knots are transformed into each other by $C_k$-moves if and only if they have the same Vassiliev...