https://companal.subwiki.org/w/index.php?action=history&feed=atom&title=Winding_number_of_cycle_around_pointWinding number of cycle around point - Revision history2026-08-02T14:48:49ZRevision history for this page on the wikiMediaWiki 1.41.2https://companal.subwiki.org/w/index.php?title=Winding_number_of_cycle_around_point&diff=534&oldid=prevVipul: 2 revisions2008-05-18T19:19:37Z<p>2 revisions</p>
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</td></tr></table>Vipulhttps://companal.subwiki.org/w/index.php?title=Winding_number_of_cycle_around_point&diff=533&oldid=prevVipul: /* Definition in terms of homology classes */2008-04-20T14:42:11Z<p><span dir="auto"><span class="autocomment">Definition in terms of homology classes</span></span></p>
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<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>===Definition in terms of homology classes===</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>===Definition in terms of homology classes===</div></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;"><br></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;"><br></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>Let <math>c</math> be a cycle (a sum of loops) in <math>\mathbb{C}</math>, and <math>z_0 \in \mathbb{C}</math> be a point not lying on any of the loos comprising <math>c</math>. The '''winding number''' of <math>c</math> about <math>z_0</math> is the homology class of <math>c</<del style="font-weight: bold; text-decoration: none;">mat</del>> viewed as a cycle in <math>\mathbb{C} \setminus \{ z_0\}</math>.</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>Let <math>c</math> be a cycle (a sum of loops) in <math>\mathbb{C}</math>, and <math>z_0 \in \mathbb{C}</math> be a point not lying on any of the loos comprising <math>c</math>. The '''winding number''' of <math>c</math> about <math>z_0</math> is the homology class of <math>c</<ins style="font-weight: bold; text-decoration: none;">math</ins>> viewed as a cycle in <math>\mathbb{C} \setminus \{ z_0\}</math>.</div></td></tr>
</table>Vipulhttps://companal.subwiki.org/w/index.php?title=Winding_number_of_cycle_around_point&diff=532&oldid=prevVipul: New page: ==Definition== ===Definition in terms of complex integrals=== Let <math>c</math> be a cycle (a sum of loops) in <math>\mathbb{C}</math> and <math>z_0 \in \mathbb{C}</math> be a point not...2008-04-20T14:41:43Z<p>New page: ==Definition== ===Definition in terms of complex integrals=== Let <math>c</math> be a cycle (a sum of loops) in <math>\mathbb{C}</math> and <math>z_0 \in \mathbb{C}</math> be a point not...</p>
<p><b>New page</b></p><div>==Definition==<br />
<br />
===Definition in terms of complex integrals===<br />
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Let <math>c</math> be a cycle (a sum of loops) in <math>\mathbb{C}</math> and <math>z_0 \in \mathbb{C}</math> be a point not lying on any of the loops comprising <math>c</math>. Then, the '''winding number''' of <math>c</math> about <math>z_0</math>, denoted <math>n(c;z_0)</math>, is defined by:<br />
<br />
<math>n(c;z_0) := \frac{1}{2\pi i }\int \frac{dz}{z - z_0}</math><br />
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===Definition in terms of homology classes===<br />
<br />
Let <math>c</math> be a cycle (a sum of loops) in <math>\mathbb{C}</math>, and <math>z_0 \in \mathbb{C}</math> be a point not lying on any of the loos comprising <math>c</math>. The '''winding number''' of <math>c</math> about <math>z_0</math> is the homology class of <math>c</mat> viewed as a cycle in <math>\mathbb{C} \setminus \{ z_0\}</math>.</div>Vipul