In this paper, we study the word map w : SU(2) ×SU(2) →SU(2), where w is a word in the free group F of rank 2. We give a necessary and sufficient condition for the surjectivity of the word map by using the trace polynomials. As applications of our method, we give example of word w∉F(2) for which the word map is not surjective. For families of words belonging to F(2) of the form [[a,b], [a,bn]] and [[a,b], [a2,bn]], we can tell whether the word map is surjective or not.

中文翻译：

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关于SU(2)上某些词图的超射性

在本文中，我们研究了词图w ： 苏(2) ×苏(2) →苏(2),在哪里w是自由组中的一个词F秩为 2。我们利用迹多项式给出了词图的满射性的充要条件。作为我们方法的应用，我们给出了单词的例子w∉F(2)词图不是满射的。对于属于单词的家庭F(2)形式的[[一种,b], [一种,bn]]和[[一种,b], [一种2,bn]],我们可以判断 word map 是否是满射的。