A rational invariant for knot crossings

Lee, Youn

doi:10.1090/S0002-9939-98-05024-2

A rational invariant for knot crossings
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by Youn W. Lee

Proc. Amer. Math. Soc. 126 (1998), 3385-3392

DOI: https://doi.org/10.1090/S0002-9939-98-05024-2

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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.

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