2-Adjacency between pretzel links and the trivial link

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• 作者：Zhi-Xiong Tao ^{tomzhx@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：57M25
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：214
• 期：Complete
• 页码：186-191
• 全文大小：257 K

文摘

We study 2-adjacency between a 3-strand pretzel link with two components and the trivial link, and whether the trivial knot is 2-adjacent to a pretzel knot. By investigating mainly the coefficients of their Conway polynomials, Jones polynomials and etc., we show that any nontrivial pretzel link with two-components is not 2-adjacent to the trivial link, and vice versa. Moreover, we also show that the trivial knot is not 2-adjacent to any nontrivial pretzel knot.