7 citations · 12 across the 7 of their papers we have counts for
7 papers
Singularities of translation surfaces under the linearly dependent condition in Euclidean 3-space
Tomonori Fukunaga, Nozomi Nakatsuyama, Masatomo Takahashi
We investigated singular points of translation surfaces under the linearly independent condition. In this paper, as completion, we investigate singular points of translation surfac…
Lifting link invariants by functors on nanophrases
Tomonori Fukunaga, Noboru Ito
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 f…
Simplified numerical form of universal finite type invariant of Gauss words
Tomonori Fukunaga, Takayuki Yamaguchi, Takaaki Yamanoi
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…
On Generalization of Homotopy of Words and Its Applications
Tomonori Fukunaga
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 t…
Homotopy Classification of Generalized Phrases in Turaev's Theory of Words
Tomonori Fukunaga
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…
Homotopy classification of nanophrases with less than or equal to four letters
Tomonori Fukunaga
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…
Khovanov homology and words
Tomonori Fukunaga, Noboru Ito
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 int…