Arf Invariant of A Knot - Definition By Alexander Polynomial

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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