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0708-1300/Homework Assignment 8 - Revision history
2024-03-29T15:35:33Z
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Drorbn at 14:51, 24 January 2008
2008-01-24T14:51:28Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 14:51, 24 January 2008</td>
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<tr><td class='diff-marker'>−</td><td style="color:black; 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;">{{In Preparation}}</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Reading==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Reading==</div></td></tr>
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Drorbn
http://drorbn.net/index.php?title=0708-1300/Homework_Assignment_8&diff=6215&oldid=prev
Drorbn at 14:49, 24 January 2008
2008-01-24T14:49:46Z
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Doing==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Doing==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>'''Just one problem.''' Let <math>K</math> be a knot in <math>{\mathbb R}^3</math> presented by a planar diagram <math>D</math>. With a massive use of Van-Kampen's theorem, show that the fundamental group of the complement of <math>K</math> has a presentation (the "Wirtinger" <del class="diffchange diffchange-inline">[http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Wirtinger.html] [http://en.wikipedia.org/wiki/Wirtinger] </del>presentation) with one generator for each edge of <math>D</math> and two relations for each crossing of <math>D</math>, as indicated in the figure below.</div></td><td class='diff-marker'>+</td><td style="color:black; 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>'''Just one problem.''' Let <math>K</math> be a knot in <math>{\mathbb R}^3</math> presented by a planar diagram <math>D</math>. With a massive use of Van-Kampen's theorem, show that the fundamental group of the complement of <math>K</math> has a presentation (the "Wirtinger" presentation) with one generator for each edge of <math>D</math> and two relations for each crossing of <math>D</math>, as indicated in the figure below.</div></td></tr>
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Drorbn
http://drorbn.net/index.php?title=0708-1300/Homework_Assignment_8&diff=6213&oldid=prev
Drorbn at 14:44, 24 January 2008
2008-01-24T14:44:07Z
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<p><b>New page</b></p><div>{{0708-1300/Navigation}}<br />
{{In Preparation}}<br />
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==Reading==<br />
Read, reread and rereread your notes to this point, and make sure that you really, really really, really really really understand everything in them. Do the same every week!<br />
<br />
==Doing==<br />
'''Just one problem.''' Let <math>K</math> be a knot in <math>{\mathbb R}^3</math> presented by a planar diagram <math>D</math>. With a massive use of Van-Kampen's theorem, show that the fundamental group of the complement of <math>K</math> has a presentation (the "Wirtinger" [http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Wirtinger.html] [http://en.wikipedia.org/wiki/Wirtinger] presentation) with one generator for each edge of <math>D</math> and two relations for each crossing of <math>D</math>, as indicated in the figure below.<br />
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[[Image:0708-1300-WirtingerExample.png]]<br />
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==Due Date==<br />
This assignment is due in class on Thursday February 7, 2008.</div>
Drorbn