Definition By Alexander Polynomial
This approach to the Arf invariant is by Raymond Robertello. Let
be the Alexander polynomial of the knot. Then the Arf invariant is the residue of
modulo 2, where r = 0 for n odd, and r = 1 for n even.
Kunio Murasugi proved that the Arf invariant is zero if and only if Δ(−1) ±1 modulo 8.
Read more about this topic: Arf Invariant Of A Knot
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