https://drorbn.net/index.php?action=history&feed=atom&title=Notes_for_AKT-090924-1%2F0%3A30%3A11 2026-05-04T20:50:33Z Revision history for this page on the wiki MediaWiki 1.39.6 https://drorbn.net/index.php?title=Notes_for_AKT-090924-1/0:30:11&diff=10672&oldid=prev 2011-09-15T13:08:48Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 09:08, 15 September 2011</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="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;"><div><del style="font-weight: bold; text-decoration: none;">Bijection</del> between knots on a circle and knots on a <del style="font-weight: bold; text-decoration: none;">(</del>long<del style="font-weight: bold; text-decoration: none;">)</del> line<del style="font-weight: bold; text-decoration: none;">.</del></div></td> <td class="diff-marker" data-marker="+"></td> <td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">'''Claim 1''': There is a bijection</ins> between<ins style="font-weight: bold; text-decoration: none;"> round knots (i.e.</ins> knots on a circle<ins style="font-weight: bold; text-decoration: none;">)</ins> and<ins style="font-weight: bold; text-decoration: none;"> long knots (i.e.</ins> knots on a long line<ins style="font-weight: bold; text-decoration: none;">):</ins></div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="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;"><div>: &lt;math&gt;\mathcal{K}(\bigcirc)=\mathcal{K}(|)&lt;/math&gt;</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="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;"><br /></td> <td class="diff-marker"></td> <td style="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;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="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;"><div><del style="font-weight: bold; text-decoration: none;">The</del> <del style="font-weight: bold; text-decoration: none;">long</del> <del style="font-weight: bold; text-decoration: none;">like</del> is an <del style="font-weight: bold; text-decoration: none;">Abelian</del> monoid.</div></td> <td class="diff-marker" data-marker="+"></td> <td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">'''Claim</ins> <ins style="font-weight: bold; text-decoration: none;">2''':</ins> <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;\mathcal{K}(|)&lt;/math&gt;</ins> is an <ins style="font-weight: bold; text-decoration: none;">abelian</ins> monoid.</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="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;"><br /></td> <td class="diff-marker"></td> <td style="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;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="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;"><div>Remark: I think it's worth checking that the map from circle to line is independent of the choice of point to 'open up' and the path we 'pull out' the two ends after cutting. However it is indeed independent.</div></td> <td class="diff-marker" data-marker="+"></td> <td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">''</ins>Remark<ins style="font-weight: bold; text-decoration: none;">''</ins>: I think it's worth checking that the map from circle to line is independent of the choice of point to 'open up' and the path we 'pull out' the two ends after cutting. However it is indeed independent.</div></td> </tr> </table>

Iva https://drorbn.net/index.php?title=Notes_for_AKT-090924-1/0:30:11&diff=7912&oldid=prev 2009-09-25T04:43:28Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:43, 25 September 2009</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 2:</td> <td colspan="2" class="diff-lineno">Line 2:</td> </tr> <tr> <td class="diff-marker"></td> <td style="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;"><br /></td> <td class="diff-marker"></td> <td style="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;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="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;"><div>The long like is an Abelian monoid.</div></td> <td class="diff-marker"></td> <td style="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;"><div>The long like is an Abelian monoid.</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="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;"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="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;"><div>Remark: I think it's worth checking that the map from circle to line is independent of the choice of point to 'open up' and the path we 'pull out' the two ends after cutting. However it is indeed independent.</div></td> </tr> </table>

Conan777 https://drorbn.net/index.php?title=Notes_for_AKT-090924-1/0:30:11&diff=7910&oldid=prev 2009-09-25T04:34:38Z

<p></p> <p><b>New page</b></p><div>Bijection between knots on a circle and knots on a (long) line.<br /> <br /> The long like is an Abelian monoid.</div>

Conan777