On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links
Abstract
There are many studies about twisted Alexander invariants for knots and links, but calculations of twisted Alexander invariants for spatial graphs, handlebody-knots, and surface-links have not been demonstrated well. In this paper, we give some remarks to calculate the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links, and observe their behaviors. For spatial graphs, we calculate the invariants of Suzuki's theta-curves and show that the invariants are nontrivial for Suzuki's theta-curves whose Alexander ideals are trivial. For handlebody-knots, we give a remark on abelianizations and calculate the invariant of the handlebody-knots up to six crossings. For surface-links, we correct Yoshikawa's table and calculate the invariants of the surface-links in the table.
Keywords
Cite
@article{arxiv.1503.07969,
title = {On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links},
author = {Atsushi Ishii and Ryo Nikkuni and Kanako Oshiro},
journal= {arXiv preprint arXiv:1503.07969},
year = {2020}
}
Comments
17 pages, 1 figure