Signature of a knot

The signature s(K) of a knot K can be defined using the skein relationship

$s(unknot) = 0\,$

$s(K_+) - s(K_-) \in \left \{0, 2\right \},$

and

$4|s(K) \leftrightarrow \nabla(K)(2i) > 0$

where $\nabla(K)$ is the Knot polynomial and $\nabla(K)(2i)$ is an odd number.

Many unknotting numbers can be determined using a knot's signature.

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07-14-2008 23:18:10
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