I found the statement this theorem on wikipedia but I could not get any further information. How is this possible? Could you please give me some further reference? Thank you.
2026-03-29 18:33:26.1774809206
Is any (Laurent)polynomial that is symmetric and $f(1)=1$ the Alexander polynomial of some knot?
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See Theorem 5 on page 171 of Rolfsen's Knots and Links. The general idea is that you can do surgery in the complement of the unknot, where the surgery solid torus is knotted according to the coefficients of the Laurent polynomial. When you have a surgery curve that has linking number $0$ with an unknot, the infinite cyclic cover of the resulting knot after surgery has a nice description.
A reference with another description of these sorts of infinite cyclic covers is Lickorish's An Introduction to Knot Theory, page 70.