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pro vyhledávání: '"Mizusawa, Atsuhiko"'
Autor:
Kotorii, Yuka, Mizusawa, Atsuhiko
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 to spatial graphs and it is called component-homotopy. The link-homotop
Externí odkaz:
http://arxiv.org/abs/2312.12822
Autor:
Kotorii, Yuka, Mizusawa, Atsuhiko
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 for string links. In this paper, we calculated the actions of the par
Externí odkaz:
http://arxiv.org/abs/2212.14502
Akademický článek
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Autor:
Kotorii, Yuka, Mizusawa, Atsuhiko
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 were classified by Levine with enormous algebraic computations. We modif
Externí odkaz:
http://arxiv.org/abs/1910.08653
Autor:
Kotorii, Yuka, Mizusawa, Atsuhiko
A handlebody-link is a disjoint union of embeddings of handlebodies in $S^3$ and an HL-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes. The second author and Ryo Nikkuni classified the set of HL-homotopy cla
Externí odkaz:
http://arxiv.org/abs/1603.09067
Autor:
Mizusawa, Atsuhiko, Murakami, Jun
We define invariants for colored oriented spatial graphs by generalizing CM invariants, which were defined via non-integral highest weight representations of $U_q(sl_2)$. We apply the same method to define Yokota's invariants, and we call these invar
Externí odkaz:
http://arxiv.org/abs/1502.04477
Publikováno v:
Graphs Combin. 32 (2016), no. 3, 1117-1124
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 answer of L.~Nebesk$\acute{\mbox{y}}$'s question, "Does there exists
Externí odkaz:
http://arxiv.org/abs/1409.3711
Autor:
Mizusawa, Atsuhiko, Nikkuni, Ryo
Publikováno v:
Topology Appl. 196 (2015), Part B, 710--718
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 classification of all 2-component spatial graphs up to neighborhood hom
Externí odkaz:
http://arxiv.org/abs/1212.6629
Autor:
Mizusawa, Atsuhiko
Publikováno v:
Proc. Japan Acad. Ser. A Math. Sci. Vol. 89, No. 4 (2013), 60-62
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 natural homomorphism from the first homology group of a component to that
Externí odkaz:
http://arxiv.org/abs/1210.7408
Autor:
Mizusawa, Atsuhiko, Murakami, Jun
Publikováno v:
Journal of Knot Theory and Its Ramifications, Volume 22, Issue 11, October 2013
We construct quantum $\mathcal{U}_q(\mathfrak{sl}_{\,2})$ type invariants for handlebody-knots in the 3-sphere $S^3$. A handlebody-knot is an embedding of a handlebody in a 3-manifold. These invariants are linear sums of Yokota's invariants for color
Externí odkaz:
http://arxiv.org/abs/1112.2719