https://diffgeom.subwiki.org/w/index.php?action=history&feed=atom&title=Isotopy_of_immersions
Isotopy of immersions - Revision history
2026-07-03T16:04:26Z
Revision history for this page on the wiki
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https://diffgeom.subwiki.org/w/index.php?title=Isotopy_of_immersions&diff=786&oldid=prev
Vipul: 2 revisions
2008-05-18T19:47:42Z
<p>2 revisions</p>
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:47, 18 May 2008</td>
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Vipul
https://diffgeom.subwiki.org/w/index.php?title=Isotopy_of_immersions&diff=785&oldid=prev
Vipul at 23:51, 3 April 2008
2008-04-03T23:51:31Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:51, 3 April 2008</td>
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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>* <math>F(p,0) = f_0(p)</math> and <math>F(p,1) = f_1(p)</math>: In other words <math>F</math> is a homotopy from <math>f_0</math> to <math>f_1</math></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>* <math>F(p,0) = f_0(p)</math> and <math>F(p,1) = f_1(p)</math>: In other words <math>F</math> is a homotopy from <math>f_0</math> to <math>f_1</math></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;"><div>* For each <math>t</math>, the map from <math>M</math> to <math>\N</math> given by <math>p \mapsto f(p,t)</math> is an immersion</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>* For each <math>t</math>, the map from <math>M</math> to <math>\N</math> given by <math>p \mapsto f(p,t)</math> is an immersion</div></td></tr>
<tr><td colspan="2" class="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><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="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><ins style="font-weight: bold; text-decoration: none;">==Facts==</ins></div></td></tr>
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<tr><td colspan="2" class="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><ins style="font-weight: bold; text-decoration: none;">* [[Immersions in Euclidean space are isotopic in its square]]</ins></div></td></tr>
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Vipul
https://diffgeom.subwiki.org/w/index.php?title=Isotopy_of_immersions&diff=784&oldid=prev
Vipul: New page: ==Definition== Suppose <math>M, N</math> are smooth manifolds of dimensions <math>m, n</math> and <math>f_0,f_1: M \to N</math> are two smooth immersions. An isotopy from <math>f_...
2008-04-03T23:50:29Z
<p>New page: ==Definition== Suppose <math>M, N</math> are <a href="/wiki/Smooth_manifold" class="mw-redirect" title="Smooth manifold">smooth manifolds</a> of dimensions <math>m, n</math> and <math>f_0,f_1: M \to N</math> are two smooth <a href="/wiki/Immersion" title="Immersion">immersions</a>. An isotopy from <math>f_...</p>
<p><b>New page</b></p><div>==Definition==<br />
<br />
Suppose <math>M, N</math> are [[smooth manifold]]s of dimensions <math>m, n</math> and <math>f_0,f_1: M \to N</math> are two smooth [[immersion]]s. An isotopy from <math>f_0</math> to <math>f_1</math> is a map <math>F:M \times I \to \R^n</math> such that the following hold:<br />
<br />
* <math>F</math> is a [[smooth map]]<br />
* <math>F(p,0) = f_0(p)</math> and <math>F(p,1) = f_1(p)</math>: In other words <math>F</math> is a homotopy from <math>f_0</math> to <math>f_1</math><br />
* For each <math>t</math>, the map from <math>M</math> to <math>\N</math> given by <math>p \mapsto f(p,t)</math> is an immersion</div>
Vipul