Year: 2021
Type: article
Abstract: Using the techniques on annulus twists, we observe that $6_3$ has infinitely many non-characterizing slopes, which affirmatively answers a question by Baker and Motegi. Furthermore, we prove that the knots $6_2$, $6_3$, $7_6$, $7_7$, $8_1$, $8_3$, $8_4$, $8_6$, $8_7$, $8_9$, $8_{10}$, $8_{11}$, $8_{12}$, $8_{13}$, $8_{14}$, $8_{17}$, $8_{20}$ and $8_{21}$ have infinitely many non-characterizing slopes. We also introduce the notion of trivial annulus twists and give some possible applications. Finally, we completely determine which knots have special annulus presentations up to 8-crossings.
Source: Kodai Mathematical Journal
DOI: 10.2996/kmj/kmj44301
Authors: Tetsuya Abe, Keiji Tagami
Institutions: Ritsumeikan University, National Fisheries University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3208165752