https://katlas.org/api.php?action=feedcontributions&feedformat=atom&user=CvaroUc4tr 2026-04-25T09:06:57Z User contributions MediaWiki 1.39.6 https://katlas.org/index.php?title=Talk:The_Multivariable_Alexander_Polynomial&diff=1693695 2009-05-22T09:55:15Z

<p>CvaroUc4tr: </p> <hr /> <div>http://www.textcacelcn.com <br /> Regarding this comment:<br /> <br /> :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.<br /> <br /> The multivariable Alexander polynomial is zero precisely when &lt;math&gt;H_1&lt;/math&gt; of the universal Abelian cover has non-zero rank (as a module over the group-ring of covering transformations). Equivalently, if &lt;math&gt;H_2&lt;/math&gt; of the universal Abelian cover is non-trivial. In the [[L10n36]] case, &lt;math&gt;H_2&lt;/math&gt; 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</div>

CvaroUc4tr