Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A rational invariant for knot crossings

Author(s): Youn W. Lee
Journal: Proc. Amer. Math. Soc. 126 (1998), 3385-3392.
MSC (1991): Primary 57M25
MathSciNet review: 1621977
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Abstract: A rational number-valued invariant is constructed for the crossings of knot projections. The invariant completely determines the signature and (signed) determinant of the knot obtained by changing the crossing. In particular, if the invariant is not 0, then the new knot is distinct from the old one.

References:

1.: J. Milnor, Morse Theory, Annals of Math. Studies (51), Princeton Univ. Press, 1963. MR 29:634
2.: K. Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965), 387-422. MR 30:1506
3.: D. Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish Press, 1976. MR 58:24236; MR 95c:57018
4.: M. Scharlemann, Smooth spheres in $\mathbb{R}^4$ with four critical points are standard, Invent. Math. 79 (1985), 125-141. MR 86e:57010
5.: H. F. Trotter, On $S$ -equivalence of Seifert matrices, Invent. Math. 20 (1973), 173-207. MR 58:31100

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