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Invariants from the Seifert Matrix

  • Kunio Murasugi
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

In order to find a knot (or link) invariant from a Seifert matrix, we need to look for something that will not change under the operations Λ1 and \(\Lambda^{\pm 1}_2\), defined in Theorem 5.4.1. We will see in this chapter that the Alexander polynomial is such an invariant. The Alexander polynomial is not the only important invariant that we can extricate from the Seifert matrix, the signature of a link can also be defined from it. In addition to defining these two invariants we shall, in this chapter, prove some of their basic characteristics. Nota bene, throughout this chapter we shall assume all the knots and links are oriented.

Keywords

Laurent Polynomial Alexander Polynomial Seifert Surface Skein Relation Integer Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Kunio Murasugi
    • 1
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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