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April 2018 On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links
Atsushi Ishii, Ryo Nikkuni, Kanako Oshiro
Osaka J. Math. 55(2): 297-313 (April 2018).

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.

Citation

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Atsushi Ishii. Ryo Nikkuni. Kanako Oshiro. "On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links." Osaka J. Math. 55 (2) 297 - 313, April 2018.

Information

Published: April 2018
First available in Project Euclid: 18 April 2018

zbMATH: 06870390
MathSciNet: MR3787746

Subjects:
Primary: 57M05
Secondary: 57M15, 57Q45

Rights: Copyright © 2018 Osaka University and Osaka City University, Departments of Mathematics

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Vol.55 • No. 2 • April 2018
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