ON CALCULATIONS OF THE TWISTED ALEXANDER IDEALS FOR SPATIAL GRAPHS, HANDLEBODY-KNOTS AND SURFACE-LINKS

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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 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.

Journal

  • Osaka Journal of Mathematics

    Osaka Journal of Mathematics 55(2), 297-313, 2018-04

    Osaka University and Osaka City University, Departments of Mathematics

Codes

  • NII Article ID (NAID)
    120006478934
  • NII NACSIS-CAT ID (NCID)
    AA00765910
  • Text Lang
    ENG
  • Article Type
    departmental bulletin paper
  • ISSN
    0030-6126
  • Data Source
    IR 
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