https://drorbn.net/index.php?action=history&feed=atom&title=Notes_for_AKT-140108%2F0%3A24%3A50 2026-05-09T23:56:24Z Revision history for this page on the wiki MediaWiki 1.39.6 https://drorbn.net/index.php?title=Notes_for_AKT-140108/0:24:50&diff=16555&oldid=prev 2018-05-31T03:08:22Z

<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 23:08, 30 May 2018</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"></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>I am still not clear on why the image of the unlink is the equator of the sphere. I am wandering why not any other circle above or below the equator. Do we homotop the image to the equator?</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>I am still not clear on why the image of the unlink is the equator of the sphere. I am wandering why not any other circle above or below the equator. Do we homotop the image to the equator?</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>Since we have assumed that the embedding is invariant, we can keep the two circles in the same plane. Then, the directional vector would always be inside of the plane. Since we are free to choose which plane we want the unlink circles to be, without loss of generality, the two circles are chosen to be in the xy-plane. Then the directional vector will not have the z-component, hence the image of the map can only be on the equator (if we choose some other planes, the image would be a great circle on &lt;math&gt;S^2&lt;/math&gt; by rotating the equator).</div></td> </tr> <!-- diff cache key drordb-drorbn_:diff:wikidiff2:1.12:old-16532:rev-16555:1.13.0 --> </table>

Donghao.ouyang https://drorbn.net/index.php?title=Notes_for_AKT-140108/0:24:50&diff=16532&oldid=prev 2018-05-24T07:55:01Z

<p>Created page with &quot;I am still not clear on why the image of the unlink is the equator of the sphere. I am wandering why not any other circle above or below the equator. Do we homotop the image t...&quot;</p> <p><b>New page</b></p><div>I am still not clear on why the image of the unlink is the equator of the sphere. I am wandering why not any other circle above or below the equator. Do we homotop the image to the equator?</div>

Leo algknt