剩余无挠幂零性、双可序性与环面链环结
Residual Torsion-Free Nilpotence, Bi-Orderability and Pretzel Knots
AI总结：
本文利用 Mayland 技术证明若干亏格一及高亏格环面链环结的纽结群双可序，首次给出非纤维化或非交错纽结的双可序例子。
摘要：
纽结群的交换子群的剩余无挠幂零性在研究纽结群的双可序性中起着关键作用。Mayland 发展的一种技术利用 Baumslag 的工作，为纽结群的交换子群是剩余无挠幂零的提供了充分条件。在本文中，我们将 Mayland 的技术应用于几个亏格为一的环面链环结以及一个具有任意高亏格的环面链环结族。由此，我们获得了大量具有双可序纽结群的纽结的新例子。这些是首批非纤维化或非交错纽结具有双可序纽结群的例子。
英文摘要：
The residual torsion-free nilpotence of the commutator subgroup of a knot group has played a key role in studying the bi-orderability of knot groups. A technique developed by Mayland provides a sufficient condition for the commutator subgroup of a knot group to be residually-torsion-free nilpotent using work of Baumslag. In this paper, we apply Mayland's technique to several genus one pretzel knots and a family of pretzel knots with arbitrarily high genus. As a result, we obtain a large number of new examples of knots with bi-orderable knot groups. These are the first examples of bi-orderable knot groups for knots which are not fibered or alternating.
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。
