Turaev词论中广义短语的同伦分类
Homotopy Classification of Generalized Phrases in Turaev's Theory of Words
摘要：
在2005年V. Turaev介绍了理论的拓扑结构的单词和短语。Turaev在广义词和短语上定义了一种等价关系，称之为同伦。这是由纽结理论中的里德迈斯特运动提出的。然后Turaev给出了小于等于5个字母的广义词的同伦分类。本文给出了小于等于三个字母的同伦广义短语的分类。为此，我们构建了一个新的同伦不变量的nanophrases在任何$α$。
英文摘要：
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 gave the homotopy classification of generalized words with less than or equal to five letters. In this paper we give the classification of generalized phrases up to homotopy with less than or equal to three letters. To do this we construct a new homotopy invariant for nanophrases over any $α$.
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