Finite type invariants of nanowords and nanophrases
A Gibson, N Ito - Topology and its Applications, 2011 - Elsevier
Homotopy classes of nanowords and nanophrases are combinatorial generalizations of
virtual knots and links. Goussarov, Polyak and Viro defined finite type invariants for virtual …
virtual knots and links. Goussarov, Polyak and Viro defined finite type invariants for virtual …
A triple coproduct of curves and knots
N Ito, T Komatsuzaki - arXiv preprint arXiv:2203.13672, 2022 - arxiv.org
We suggest a triple coproduct $\Delta $ from one-component curves to three-component
curves on surfaces. By introducing a three-component version $\nu $ of the intersection …
curves on surfaces. By introducing a three-component version $\nu $ of the intersection …
AN INTERPRETATION OF MULTI-COMPONENT CURVES AND LINKS IN TERMS OF SINGLE COMPONENT WORDS
T Fukunaga - 2022 - projecteuclid.org
In the present paper, we give an interpretation of ordered pointed multi-component curves
and links on surfaces in terms of certain single component words called nanowords. We …
and links on surfaces in terms of certain single component words called nanowords. We …
Finite type invariants for cyclic equivalence classes of nanophrases
Y Kotorii - arXiv preprint arXiv:1112.6097, 2011 - arxiv.org
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 invariant of …
and construct the universal ones. Also, we identify the universal finite type invariant of …
[PDF][PDF] Classification of curves on surfaces and free links via homotopy theory of words and phrases
T Fukunaga - Journal of Singularities, 2012 - journalofsing.org
In this paper, we introduce Turaev's homotopy theory of words and phrases. As new results,
we give the classification of oriented ordered pointed irreducible multi-component curves on …
we give the classification of oriented ordered pointed irreducible multi-component curves on …
[PDF][PDF] Spectral sequences of colored Jones polynomials, colored Rasmussen invariants and nanophrases
N Ito - arXiv preprint arXiv:1008.4443, 2010 - Citeseer
We introduce three spectral sequences which give some expressions of colored Jones
polynomials. Each spectral sequence contains a Khovanov-type homology groups. Two of …
polynomials. Each spectral sequence contains a Khovanov-type homology groups. Two of …
On homotopy classification of phrases and its application
T Fukunaga - Demonstratio Mathematica, 2010 - degruyter.com
This paper is a survey on the recent study of homotopy theory of generalized phrases in
Turaev's theory of words and phrases. In this paper, we introduce the homotopy …
Turaev's theory of words and phrases. In this paper, we introduce the homotopy …