1 citations · 1 across the 11 of their papers we have counts for
12 papers
Implementation of the Habegger--Lin decision algorithm
Yuka Kotorii, Atsuhiko Mizusawa
Habegger and Lin gave a classification of link-homotopy classes of links in terms of that of string links modulo certain group actions. As an application, they constructed an algor…
Homotopy theories of colored links and spatial graphs
Yuka Kotorii, Atsuhiko Mizusawa
Two links are called link-homotopic if they are transformed to each other by a sequence of self-crossing changes and ambient isotopies. The notion of link-homotopy is generalized t…
Clasper presentations of Habegger-Lin's action on string links
Yuka Kotorii, Atsuhiko Mizusawa
Habegger and Lin gave a classification of the link-hmotopy classes of links as the link-homotopy classes of string links modulo the actions of conjugations and partial conjugations…
Ribbon Yetter--Drinfeld modules and tangle invariants
Kazuo Habiro, Yuka Kotorii
We define notions of pivotal and ribbon objects in a monoidal category. These constructions give pivotal or ribbon monoidal categories from a monoidal category which is not necessa…
Link-homotopy classes of 4-component links and claspers
Yuka Kotorii, Atsuhiko Mizusawa
Two links are link-homotopic if they are transformed into each other by a sequence of self-crossing changes and ambient isotopies. The link-homotopy classes of 4-component links we…
Goussarov-Polyak-Viro Conjecture for degree three case
Noboru Ito, Yuka Kotorii, Masashi Takamura
Although it is known that the dimension of the Vassiliev invariants of degree three of long virtual knots is seven, the complete list of seven distinct Gauss diagram formulas have…
Goussarov-Polyak-Viro's -equivalence and the pure virtual braid group
Yuka Kotorii
In the context of finite type invariants, Stanford introduced a family of equivalence relations on knots defined by the lower central series of the pure braid groups and characteri…
HL-homotopy of handlebody-links and Milnor's invariants
Yuka Kotorii, Atsuhiko Mizusawa
A handlebody-link is a disjoint union of embeddings of handlebodies in and an HL-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes. T…
A relation between Milnor's -invariants and HOMFLYPT polynomials
Yuka Kotorii
Polyak showed that any Milnor's -invariant of length 3 can be represented as a combination of Conway polynomials of knots obtained by certain band sum of the link compo…
Milnor invariants of length for links with vanishing Milnor invariants of length
Yuka Kotorii, Akira Yasuhara
J.-B. Meilhan and the second author showed that any Milnor -invariant of length between 3 and can be represented as a combination of HOMFLYPT polynomial of knots obta…
Finite type invariants for cyclic equivalence classes of nanophrases
Yuka Kotorii
In this paper, we define finite type invariants for cyclic equivalence classes of nanophrases and construct the universal ones. Also, we identify the universal finite type invarian…
The Milnor invariants and nanophrases
Yuka Kotorii
Two link diagrams are link homotopic if one can be transformed into the other by a sequence of Reidemeister moves and self crossing changes. Milnor introduced invariants under link…