ON CALCULATIONS OF THE TWISTED ALEXANDER IDEALS FOR SPATIAL GRAPHS, HANDLEBODY-KNOTS AND SURFACE-LINKS
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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 handlebodyknots, 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.
- Osaka Journal of Mathematics
Osaka Journal of Mathematics 55(2), 297-313, 2018-04
Osaka University and Osaka City University, Departments of Mathematics