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07-1352/Class Notes for March 20 - Revision history
2026-06-20T02:25:32Z
Revision history for this page on the wiki
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Drorbn at 15:59, 20 March 2007
2007-03-20T15:59:19Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:59, 20 March 2007</td>
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<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>* Uniqueness up to vertex operations, vaguely.</div></td>
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<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>* Uniqueness up to vertex operations, vaguely.</div></td>
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<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 group <math>{\mathcal A}^V\subset {\mathcal A}(\theta)</math> and its action on the set <math>{\mathcal Z}</math> of <math>{\mathcal A}</math>-valued algebraic knot theories.</div></td>
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<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 group <math>{\mathcal A}^V\subset {\mathcal A}(\theta)</math> and its action on the set <math>{\mathcal Z}</math> of <math>{\mathcal A}</math>-valued algebraic knot theories.</div></td>
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<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;">A</del> <del style="font-weight: bold; text-decoration: none;">word</del> about trinions (also see [[06-1350/Class Notes for Tuesday October 10]]).</div></td>
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<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;">An</ins> <ins style="font-weight: bold; text-decoration: none;">aside</ins> about trinions (also see [[06-1350/Class Notes for Tuesday October 10]]).</div></td>
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<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 group <math>{\mathcal A}^F\subset {\mathcal A}(\uparrow_2)</math> and its action on the set of all associators.</div></td>
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<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 group <math>{\mathcal A}^F\subset {\mathcal A}(\uparrow_2)</math> and its action on the set of all associators.</div></td>
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<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;">A</del> <del style="font-weight: bold; text-decoration: none;">word</del> about braided <math>\theta</math>-graphs:</div></td>
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<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;">An</ins> <ins style="font-weight: bold; text-decoration: none;">aside</ins> about braided <math>\theta</math>-graphs:</div></td>
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<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>[[Image:07-1352 A Braided Theta Graph.png|480px|center]]</div></td>
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<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>[[Image:07-1352 A Braided Theta Graph.png|480px|center]]</div></td>
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<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>:(Also see [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/BraidedThetas/index.html Dror Bar-Natan's Image Gallery: Knotted Objects: Braided Thetas].)</div></td>
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<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>:(Also see [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/BraidedThetas/index.html Dror Bar-Natan's Image Gallery: Knotted Objects: Braided Thetas].)</div></td>
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Drorbn
https://drorbn.net/index.php?title=07-1352/Class_Notes_for_March_20&diff=4484&oldid=prev
Drorbn at 15:58, 20 March 2007
2007-03-20T15:58:40Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:58, 20 March 2007</td>
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<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>'''Today's Agenda.''' The up-to-vertex-operations uniqueness of an <math>{\mathcal A}</math>-valued algebraic knot theory.</div></td>
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<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>
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<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>* Uniqueness up to vertex operations, vaguely.</div></td>
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<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>* The group <math>{\mathcal A}^V\subset {\mathcal A}(\theta)</math> and its action on the set <math>{\mathcal Z}</math> of <math>{\mathcal A}</math>-valued algebraic knot theories.</div></td>
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<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>* A word about trinions (also see [[06-1350/Class Notes for Tuesday October 10]]).</div></td>
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<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>* The group <math>{\mathcal A}^F\subset {\mathcal A}(\uparrow_2)</math> and its action on the set of all associators.</div></td>
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<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>* A word about braided <math>\theta</math>-graphs:</div></td>
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<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>[[Image:07-1352 A Braided Theta Graph.png|480px|center]]</div></td>
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<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>:(Also see [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/BraidedThetas/index.html Dror Bar-Natan's Image Gallery: Knotted Objects: Braided Thetas].)</div></td>
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<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>* A degree-by-degree construction of a twistor F and the reduction to homology.</div></td>
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<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>* Computing the homology using unitrivalent graphs and black boxes.</div></td>
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Drorbn
https://drorbn.net/index.php?title=07-1352/Class_Notes_for_March_20&diff=4482&oldid=prev
Drorbn at 15:32, 20 March 2007
2007-03-20T15:32:32Z
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<p><b>New page</b></p><div>{{07-1352/Navigation}}<br />
{{In Preparation}}</div>
Drorbn