Signature of a knot

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In mathematics, the signature of a knot K, denoted by s(K), can be defined using the skein relationship

s(\mathrm{unknot}) = 0\,
s(K_+) - s(K_-) \in \left \{0, 2\right \},

and

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

where ∇(K) is the knot polynomial and ∇(K)(2i) is an odd number. Many unknotting numbers can be determined using a knot's signature.


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