Abstract
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 investigate a generalized homotopy of nanowords and show that there is a canonical injection from the set of homotopy classes of nanophrases to the set of generalized homotopy classes of nanowords. As a corollary, the set of ordered pointed multi-component curves and links on surfaces is interpreted by the set of certain generalized homotopy classes of nanowords. We also discuss a relation between generalized homotopy of nanowords and ornaments on surfaces.
Acknowledgements
The author would like to thank Andrew Gibson for valuable comments to the first draft of this paper. The author also would like to thank the referee for helpful comments to improve the original manuscript.
Citation
Tomonori Fukunaga. "AN INTERPRETATION OF MULTI-COMPONENT CURVES AND LINKS IN TERMS OF SINGLE COMPONENT WORDS." Nihonkai Math. J. 33 (1) 25 - 38, 2022.
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