转子特征
Signature of rotors
摘要：
Tutte在图论中引入了转子。1987年，Anstee、Przytycki和Rolfsen将这一概念应用于纽结理论，作为突变的概括。在本文中，我们证明了Tristram-Levine签名是保持方向保持旋转。此外，我们证明了从Goeritz矩阵的特征多项式中得到的任何链接不变量，包括Murasugi签名，都不会因旋转而改变。在2001年，P. Traczyk证明了任何一对保持方向的旋转体的Conway多项式是重合的。但反向旋转是否保持Conway多项式仍是一个悬而未决的问题。我们证明了存在一对具有不同Conway多项式的反向转动子。这提供了对问题的消极解决方案。
英文摘要：
Rotors were introduced in Graph Theory by W.Tutte. The concept was adapted to Knot Theory as a generalization of mutation by Anstee, Przytycki and Rolfsen in 1987. In this paper we show that Tristram-Levine signature is preserved by orientation-preserving rotations. Moreover, we show that any link invariant obtained from the characteristic polynomial of Goeritz matrix, including Murasugi signature, is not changed by rotations. In 2001, P. Traczyk showed that the Conway polynomials of any pair of orientation-preserving rotants coincide. But it was still an open problem if an orientation-reversing rotation preserves Conway polynomial. We show that there is a pair of orientation-reversing rotants with different Conway polynomials. This provides a negative solution to the problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
