6 citations · 16 across the 10 of their papers we have counts for
10 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…
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…
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…
Yokota type invariants derived from non-integral highest weight representations of
Atsuhiko Mizusawa, Jun Murakami
We define invariants for colored oriented spatial graphs by generalizing CM invariants, which were defined via non-integral highest weight representations of . We apply…
A construction of smooth travel groupoids on finite graphs
Diogo Kendy Matsumoto, Atsuhiko Mizusawa
A travel groupoid is an algebraic system related with graphs. In this paper, we give an algorithm to construct smooth travel groupoids for any finite graph. This algorithm gives an…
A homotopy classification of two-component spatial graphs up to neighborhood equivalence
Atsuhiko Mizusawa, Ryo Nikkuni
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete c…
Linking numbers for handlebody-links
Atsuhiko Mizusawa
As a generalization of the linking number, we construct a set of invariant numbers for two-component handlebody-links. These numbers are elementary divisors associated with the nat…
Invariants of Handlebody-Knots via Yokota's Invariants
Atsuhiko Mizusawa, Jun Murakami
We construct quantum type invariants for handlebody-knots in the 3-sphere . A handlebody-knot is an embedding of a handlebody in a 3-manif…