Výsledky vyhledávání - "Fukunaga, Tomonori"

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Lifting link invariants by functors on nanophrases

Nanophrases have a filtered structure consisting of an infinite number of categories, and each category has a homotopy structure. Among these categories, the one that we are most familiar with is the category of links. Interestingly, the category in

Externí odkaz: http://arxiv.org/abs/2401.04506

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Simplified numerical form of universal finite type invariant of Gauss words

Autor: Fukunaga, Tomonori, Yamaguchi, Takayuki, Yamanoi, Takaaki

In the present paper, we study the finite type invariants of Gauss words. In the Polyak algebra techniques, we reduce the determination of the group structure to transformation of a matrix into its Smith normal form and we give the simplified form of

Externí odkaz: http://arxiv.org/abs/1209.0287

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On Generalization of Homotopy of Words and Its Applications

Autor: Fukunaga, Tomonori

V. Turaev introduced the theory of topology of words and phrases in 2005. This is a combinatorialy extension of the theory of virtual knots and links. In this paper we generalize the notion of homotopy of words and phrases and we give geometric meani

Externí odkaz: http://arxiv.org/abs/0908.2899

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Homotopy Classification of Generalized Phrases in Turaev's Theory of Words

Autor: Fukunaga, Tomonori

In 2005 V. Turaev introduced the theory of topology of words and phrases. Turaev defined an equivalence relation on generalized words and phrases which is called homotopy. This is suggested by the Reidemeister moves in the knot theory. Then Turaev ga

Externí odkaz: http://arxiv.org/abs/0904.4206

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Homotopy classification of nanophrases with less than or equal to four letters

Autor: Fukunaga, Tomonori

In this paper we give the stable classification of ordered, pointed, oriented multi-component curves on surfaces with minimal crossing number less than or equal to 2 such that any equivalent curve has no simply closed curves in its components. To do

Externí odkaz: http://arxiv.org/abs/0904.3478

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Khovanov homology and words

Autor: Fukunaga, Tomonori, Ito, Noboru

This paper is concerned with nanowords, a generalization of links, introduced by Turaev. It is shown that the system of bigraded homology groups is an invariant of nanowords by introducing a new notion. This paper gives two examples which show the in

Externí odkaz: http://arxiv.org/abs/0901.3956

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Akademický článek

Evolutes and Involutes of Frontals in the Euclidean Plane

Autor: Fukunaga Tomonori, Takahashi Masatomo

Publikováno v: Demonstratio Mathematica, Vol 48, Iss 2, Pp 147-166 (2015)

We have already defined the evolutes and the involutes of fronts without inflection points. For regular curves or fronts, we can not define the evolutes at inflection points. On the other hand, the involutes can be defined at inflection points. In th

Externí odkaz: https://doaj.org/article/d19b9fc27b344069993e47652ec62127