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	<id>https://drorbn.net/index.php?action=history&amp;feed=atom&amp;title=Notes_for_AKT-090915%2F0%3A03%3A24</id>
	<title>Notes for AKT-090915/0:03:24 - Revision history</title>
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	<updated>2026-05-18T01:11:17Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://drorbn.net/index.php?title=Notes_for_AKT-090915/0:03:24&amp;diff=10604&amp;oldid=prev</id>
		<title>Iva at 17:36, 30 August 2011</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=Notes_for_AKT-090915/0:03:24&amp;diff=10604&amp;oldid=prev"/>
		<updated>2011-08-30T17:36:00Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 13:36, 30 August 2011&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Review and additions to last class, corrections:&lt;/div&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Review and additions to last class, corrections:&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Jones polynomial is usually normalized by diving &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the&lt;/del&gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&lt;/del&gt;&amp;lt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&lt;/del&gt; of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;an&lt;/del&gt; unknot (i.e. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;divide&lt;/del&gt; by an additional factor of &amp;lt;math&amp;gt;d&amp;lt;/math&amp;gt;).&lt;/div&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;#&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; The&lt;/ins&gt; Jones polynomial is usually normalized by diving &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;by&lt;/ins&gt; &amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\left\langle \bigcirc \right\rangle&amp;lt;/math&amp;gt;, the bracket&lt;/ins&gt; of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the&lt;/ins&gt; unknot (i.e. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;dividing&lt;/ins&gt; by an additional factor of &amp;lt;math&amp;gt;d&amp;lt;/math&amp;gt;).&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# We can prove &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;all&lt;/del&gt; knot &amp;lt;math&amp;gt;K&amp;lt;/math&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; has&lt;/del&gt; &amp;lt;math&amp;gt;J(K)&amp;lt;/math&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;being&lt;/del&gt; a polynomial of &amp;lt;math&amp;gt;A^4&amp;lt;/math&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;,&lt;/del&gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;hence&lt;/del&gt; we substitute &amp;lt;math&amp;gt;A=q^{1/4}&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# We can prove &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;that for any&lt;/ins&gt; knot &amp;lt;math&amp;gt;K&amp;lt;/math&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;,&lt;/ins&gt; &amp;lt;math&amp;gt;J(K)&amp;lt;/math&amp;gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;is&lt;/ins&gt; a polynomial of &amp;lt;math&amp;gt;A^4&amp;lt;/math&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;.&lt;/ins&gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Hence,&lt;/ins&gt; we&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; can&lt;/ins&gt; substitute &amp;lt;math&amp;gt;A=q^{1/4}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/math&amp;gt; to get a Laurent polynomial in &amp;lt;math&amp;gt;q&lt;/ins&gt;&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;

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&lt;/table&gt;</summary>
		<author><name>Iva</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=Notes_for_AKT-090915/0:03:24&amp;diff=7771&amp;oldid=prev</id>
		<title>Drorbn at 10:21, 16 September 2009</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=Notes_for_AKT-090915/0:03:24&amp;diff=7771&amp;oldid=prev"/>
		<updated>2009-09-16T10:21:11Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 06:21, 16 September 2009&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Review and additions to last class, corrections:&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Review and additions to last class, corrections: 1.&lt;/del&gt; Jones polynomial is usually normalized by diving the &#039;&amp;lt;&amp;gt;&#039; of an unknot (i.e. divide by an additional factor of d)&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;  2&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;We can prove all knot K has J(K) being a polynomial of A^4, hence we substitute A=q^{1/4}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;#&lt;/ins&gt; Jones polynomial is usually normalized by diving the &#039;&amp;lt;&amp;gt;&#039; of an unknot (i.e. divide by an additional factor of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;&lt;/ins&gt;d&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/math&amp;gt;&lt;/ins&gt;).&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# We can prove all knot &amp;lt;math&amp;gt;K&amp;lt;/math&amp;gt; has &amp;lt;math&amp;gt;J(K)&amp;lt;/math&amp;gt; being a polynomial of &amp;lt;math&amp;gt;A^4&amp;lt;/math&amp;gt;, hence we substitute &amp;lt;math&amp;gt;A=q^{1/4}&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;

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&lt;/table&gt;</summary>
		<author><name>Drorbn</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=Notes_for_AKT-090915/0:03:24&amp;diff=7734&amp;oldid=prev</id>
		<title>Conan777 at 02:18, 16 September 2009</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=Notes_for_AKT-090915/0:03:24&amp;diff=7734&amp;oldid=prev"/>
		<updated>2009-09-16T02:18:29Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;Review and additions to last class, corrections: 1. Jones polynomial is usually normalized by diving the &amp;#039;&amp;lt;&amp;gt;&amp;#039; of an unknot (i.e. divide by an additional factor of d)  2.We can prove all knot K has J(K) being a polynomial of A^4, hence we substitute A=q^{1/4}&lt;/div&gt;</summary>
		<author><name>Conan777</name></author>
	</entry>
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