https://katlas.org/index.php?action=history&feed=atom&title=Notes_for_10_132%27s_three_dimensional_invariants 2026-04-07T21:47:27Z Revision history for this page on the wiki MediaWiki 1.39.6 https://katlas.org/index.php?title=Notes_for_10_132%27s_three_dimensional_invariants&diff=1691676&oldid=prev 2008-01-12T21:24:32Z

<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 17:24, 12 January 2008</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>10<del style="font-weight: bold; text-decoration: none;">&lt;sub&gt;</del>132<del style="font-weight: bold; text-decoration: none;">&lt;/sub&gt;</del> is a very interesting knot from the point of view of contact geometry. In particular, it is a transversely nonsimple knot, and it was the last knot with at most 10 crossings for which the maximal Thurston-Bennequin number was calculated.</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>10<ins style="font-weight: bold; text-decoration: none;"> </ins>132<ins style="font-weight: bold; text-decoration: none;">]]</ins> is a very interesting knot from the point of view of contact geometry. In particular, it is a transversely nonsimple knot, and it was the last knot with at most 10 crossings for which the maximal Thurston-Bennequin number was calculated.</div></td> </tr> </table>

Drorbn https://katlas.org/index.php?title=Notes_for_10_132%27s_three_dimensional_invariants&diff=1689434&oldid=prev 2007-10-10T15:01:32Z

<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 11:01, 10 October 2007</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;">It</del> is <del style="font-weight: bold; text-decoration: none;">currently</del> <del style="font-weight: bold; text-decoration: none;">unknown</del> <del style="font-weight: bold; text-decoration: none;">whether</del> the <del style="font-weight: bold; text-decoration: none;">maximal</del> <del style="font-weight: bold; text-decoration: none;">Thurston-Bennequin</del> <del style="font-weight: bold; text-decoration: none;">number</del> <del style="font-weight: bold; text-decoration: none;">for</del> <del style="font-weight: bold; text-decoration: none;">the</del> <del style="font-weight: bold; text-decoration: none;">mirror</del> <del style="font-weight: bold; text-decoration: none;">10&lt;sub&gt;132&lt;/sub&gt;</del> <del style="font-weight: bold; text-decoration: none;">knot</del> is <del style="font-weight: bold; text-decoration: none;">-1</del> <del style="font-weight: bold; text-decoration: none;">or</del> <del style="font-weight: bold; text-decoration: none;">0.</del> <del style="font-weight: bold; text-decoration: none;">This</del> <del style="font-weight: bold; text-decoration: none;">is</del> the <del style="font-weight: bold; text-decoration: none;">only</del> knot with at most 10 crossings for which <del style="font-weight: bold; text-decoration: none;">this</del> <del style="font-weight: bold; text-decoration: none;">invariant</del> <del style="font-weight: bold; text-decoration: none;">is</del> <del style="font-weight: bold; text-decoration: none;">unknown</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;">10&lt;sub&gt;132&lt;/sub&gt;</ins> is <ins style="font-weight: bold; text-decoration: none;">a</ins> <ins style="font-weight: bold; text-decoration: none;">very</ins> <ins style="font-weight: bold; text-decoration: none;">interesting knot from</ins> the <ins style="font-weight: bold; text-decoration: none;">point</ins> <ins style="font-weight: bold; text-decoration: none;">of</ins> <ins style="font-weight: bold; text-decoration: none;">view</ins> <ins style="font-weight: bold; text-decoration: none;">of</ins> <ins style="font-weight: bold; text-decoration: none;">contact</ins> <ins style="font-weight: bold; text-decoration: none;">geometry.</ins> <ins style="font-weight: bold; text-decoration: none;">In</ins> <ins style="font-weight: bold; text-decoration: none;">particular, it</ins> is <ins style="font-weight: bold; text-decoration: none;">a</ins> <ins style="font-weight: bold; text-decoration: none;">transversely</ins> <ins style="font-weight: bold; text-decoration: none;">nonsimple</ins> <ins style="font-weight: bold; text-decoration: none;">knot,</ins> <ins style="font-weight: bold; text-decoration: none;">and it was</ins> the <ins style="font-weight: bold; text-decoration: none;">last</ins> knot with at most 10 crossings for which <ins style="font-weight: bold; text-decoration: none;">the</ins> <ins style="font-weight: bold; text-decoration: none;">maximal</ins> <ins style="font-weight: bold; text-decoration: none;">Thurston-Bennequin number was</ins> <ins style="font-weight: bold; text-decoration: none;">calculated</ins>.</div></td> </tr> </table>

Lng https://katlas.org/index.php?title=Notes_for_10_132%27s_three_dimensional_invariants&diff=120893&oldid=prev 2005-11-02T18:46:54Z

<p></p> <p><b>New page</b></p><div>It is currently unknown whether the maximal Thurston-Bennequin number for the mirror 10&lt;sub&gt;132&lt;/sub&gt; knot is -1 or 0. This is the only knot with at most 10 crossings for which this invariant is unknown.</div>

Lng