Talk:The Multivariable Alexander Polynomial

alchiaceld Regarding this comment:

Dror doesn't understand the multivariable Alexander polynomial well enough to give simple topological reasons for the vanishing of the said polynomial for these knots.

The multivariable Alexander polynomial is zero precisely when $H_{1}$ of the universal Abelian cover has non-zero rank (as a module over the group-ring of covering transformations). Equivalently, if $H_{2}$ of the universal Abelian cover is non-trivial. In the L10n36 case, $H_{2}$ is free on one generator, which is represented by a map of a genus 2 surface into the link complement. So far I haven't found a very appealing description of this surface, but it's there... -Ryan Budney