词同伦的推广及其应用
On Generalization of Homotopy of Words and Its Applications
摘要：
V. Turaev在2005年引入了词和短语的拓扑理论。这是虚纽结和虚链环理论的组合推广。本文推广了词和短语的同伦概念，并给出了词的广义同伦的几何意义。利用词和短语的广义同伦理论，我们将一些纳米短语的同伦不变量推广到$S$ --具有某些同伦数据$S$的词序的同伦不变量.
英文摘要：
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 meanings of the generalized homotopy of words. Moreover using the generalized homotopy theory of words and phrases, we extend some homotopy invariants of nanophrases to $S$-homotopy invariant of nanowords with some homotopy data $S$.
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