On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links

Atsushi Ishii; Ryo Nikkuni; Kanako Oshiro

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arXiv · 1503.07969

On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links

Atsushi Ishii·Ryo Nikkuni·Kanako Oshiro

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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.

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Atsushi Ishii, Ryo Nikkuni, Kanako Oshiro. 2015-03-27. On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links. https://arxiv.org/abs/1503.07969

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