2-Adjacency between pretzel links and the trivial link

摘要

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. (C) 2016 Elsevier B.V. All rights reserved.