The third term in lens surgery polynomials

Abstract

It is well-known that the second coefficient of the Alexander polynomial of any lens space knot in $S^3$ is $-1$. We show that the non-zero third coefficient condition of the Alexander polynomial of a lens space knot $K$ in $S^3$ confines the surgery to the one realized by the $(2,2g+1)$-torus knot, where $g$ is the genus of $K$. In particular, such a lens surgery polynomial coincides with ${\Delta }_{T(2,2g+1)}(t)$.

6 pages, 2 figures. Comments are welcome

Cited by in corpus (1)

• A note on changemaker lattices and Alexander polynomials of lens space knots