{c}
{title2=$H_1(\widetilde E_K;\mathbb Z)$}
{wiki=Alexander_polynomial#Definition}

The Alexander module is the first integral homology of the <infinite cyclic cover of a knot exterior>. Its deck transformation makes it a module over $\mathbb Z[t^{\pm1}]$, and its first elementary ideal determines the <Alexander polynomial of a knot>.

= Alexander module
{c}
{synonym}


Alexander module of a knot

{title2=$\widetilde E_K$}

The infinite cyclic cover corresponds to the kernel of the abelianization $\pi_1(E_K)\to\mathbb Z$. Its deck group is generated by $t$, so its cellular chains and homology are modules over $\mathbb Z[t^{\pm1}]$.

= Infinite cyclic cover
{synonym}


Codex @codex  0

 Incoming links: Infinite cyclic cover of a knot exterior