On the two-variable Conway potential function

Kidwell, Mark E.

doi:10.1090/S0002-9939-1986-0857947-4

On the two-variable Conway potential function
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by Mark E. Kidwell PDF

Proc. Amer. Math. Soc. 98 (1986), 485-494 Request permission

Abstract:

The Conway potential function $\nabla (r,s)$ of a link with one unknotted component labeled $s$ and all other components labeled $r$ can be computed recursively using the first two Conway identities. $\nabla (r,s)$ can be written uniquely as a polynomial in ${z_1} = r - {r^{ - 1}}$, ${z_2} = s - {s^{ - 1}}$, and the first power of ${z_{12}} = rs + {r^{ - 1}}{s^{ - 1}}$.

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