Drorbn - Recent changes [en]2013-05-22T00:07:06ZTrack the most recent changes to the wiki on this page.MediaWiki 1.5.7WKO2013-05-10T02:08:54Z2013-05-10T02:08:542013-05-10T02:08:54Z<p></p>
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<td colspan='2' width='50%' align='center' class='diff-otitle'>Revision as of 02:08, 10 May 2013</td>
<td colspan='2' width='50%' align='center' class='diff-ntitle'>Current revision</td>
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<tr><td colspan="2" align="left"><strong>Line 6:</strong></td>
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<tr><td> </td><td class='diff-context'>Joint with [http://www.math.toronto.edu/zsuzsi/ Zsuzsanna Dancso]</td><td> </td><td class='diff-context'>Joint with [http://www.math.toronto.edu/zsuzsi/ Zsuzsanna Dancso]</td></tr>
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<tr><td>-</td><td class='diff-deletedline'><span style="color:red"><b>Download</b></span> <span class="diffchange">{{Home Link|papers</span>/WKO/WKO.pdf<span class="diffchange">|</span>WKO.pdf<span class="diffchange">}}</span>: last updated &ge; <span class="diffchange">March 3</span>, <span class="diffchange">2012</span>. first edition: not yet.</td><td>+</td><td class='diff-addedline'><span style="color:red"><b>Download</b></span> <span class="diffchange">[http://www.math.toronto.edu/zsuzsi/research</span>/WKO/WKO.pdf WKO.pdf<span class="diffchange">]</span>: last updated &ge; <span class="diffchange">May 10</span>, <span class="diffchange">2013</span>. first edition: not yet.</td></tr>
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<tr><td> </td><td class='diff-context'>'''Abstract.''' w-Knots, and more generally, w-knotted objects (w-braids, w-tangles, etc.) make a class of knotted objects which is <u>w</u>ider but <u>w</u>eaker than their "<u>u</u>sual" counterparts. To get (say) w-knots from u-knots, one has to allow non-planar "virtual" knot diagrams, hence enlarging the the base set of knots. But then one imposes a new relation, the "overcrossings commute" relation, further beyond the ordinary collection of Reidemeister moves, making w-knotted objects a bit weaker once again.</td><td> </td><td class='diff-context'>'''Abstract.''' w-Knots, and more generally, w-knotted objects (w-braids, w-tangles, etc.) make a class of knotted objects which is <u>w</u>ider but <u>w</u>eaker than their "<u>u</u>sual" counterparts. To get (say) w-knots from u-knots, one has to allow non-planar "virtual" knot diagrams, hence enlarging the the base set of knots. But then one imposes a new relation, the "overcrossings commute" relation, further beyond the ordinary collection of Reidemeister moves, making w-knotted objects a bit weaker once again.</td></tr>
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<tr><td> </td><td class='diff-context'>The true value of w-knots, though, is likely to emerge later, for we expect them to serve as a <u>w</u>armup example for what we expect will be even more interesting - the study of <u>v</u>irtual knots, or v-knots. We expect v-knotted objects to provide the global context whose projectivization (or "associated graded structure") will be the Etingof-Kazhdan theory of deformation quantization of Lie bialgebras {{ref|EK}}. </td><td> </td><td class='diff-context'>The true value of w-knots, though, is likely to emerge later, for we expect them to serve as a <u>w</u>armup example for what we expect will be even more interesting - the study of <u>v</u>irtual knots, or v-knots. We expect v-knotted objects to provide the global context whose projectivization (or "associated graded structure") will be the Etingof-Kazhdan theory of deformation quantization of Lie bialgebras {{ref|EK}}. </td></tr>
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<tr><td>-</td><td class='diff-deletedline'>'''The paper.''' <span class="diffchange">{{Home Link|papers/WKO/WKO</span>.<span class="diffchange">pdf|WKO.pdf}}, {{Home Link|papers/WKO/WKO.zip|WKO.zip}}. (Zsuzsi's version: </span>[http://www.math.toronto.edu/zsuzsi/research/WKO/WKO.pdf WKO.pdf], [http://www.math.toronto.edu/zsuzsi/research/WKO/WKO.zip WKO.zip]).</td><td>+</td><td class='diff-addedline'>'''The paper.''' . [http://www.math.toronto.edu/zsuzsi/research/WKO/WKO.pdf WKO.pdf], [http://www.math.toronto.edu/zsuzsi/research/WKO/WKO.zip WKO.zip] <span class="diffchange">(Dror's version: {{Home Link|papers/WKO/WKO.pdf|WKO.pdf}}, {{Home Link|papers/WKO/WKO.zip|WKO.zip}}</span>).</td></tr>
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<tr><td> </td><td class='diff-context'>'''Related Mathematica Notebooks.''' "The Kishino Braid" ({{Pensieve Link|Projects/WKO/The_Kishino_Braid.nb|Source}}, {{Pensieve Link|Projects/WKO/nb/The_Kishino_Braid.pdf|PDF}}), "Dimensions" ({{Pensieve Link|Projects/WKO/Dimensions.nb|Source}}, {{Pensieve Link|Projects/WKO/nb/Dimensions|PDF}}), "wA" ({{Pensieve Link|Projects/WKO/wA.nb|Source}}, {{Pensieve Link|Projects/WKO/nb/wA.pdf|PDF}}), "InfinitesimalAlexanderModules" ({{Pensieve Link|Projects/WKO/InfinitesimalAlexanderModules.nb|Source}}, {{Pensieve Link|Projects/WKO/nb/InfinitesimalAlexanderModules.pdf|PDF}}).</td><td> </td><td class='diff-context'>'''Related Mathematica Notebooks.''' "The Kishino Braid" ({{Pensieve Link|Projects/WKO/The_Kishino_Braid.nb|Source}}, {{Pensieve Link|Projects/WKO/nb/The_Kishino_Braid.pdf|PDF}}), "Dimensions" ({{Pensieve Link|Projects/WKO/Dimensions.nb|Source}}, {{Pensieve Link|Projects/WKO/nb/Dimensions|PDF}}), "wA" ({{Pensieve Link|Projects/WKO/wA.nb|Source}}, {{Pensieve Link|Projects/WKO/nb/wA.pdf|PDF}}), "InfinitesimalAlexanderModules" ({{Pensieve Link|Projects/WKO/InfinitesimalAlexanderModules.nb|Source}}, {{Pensieve Link|Projects/WKO/nb/InfinitesimalAlexanderModules.pdf|PDF}}).</td></tr>
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