https://topospaces.subwiki.org/w/index.php?action=history&feed=atom&title=IsotopyIsotopy - Revision history2026-11-06T02:37:16ZRevision history for this page on the wikiMediaWiki 1.41.2https://topospaces.subwiki.org/w/index.php?title=Isotopy&diff=964&oldid=prevVipul: 1 revision2008-05-11T19:47:39Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://topospaces.subwiki.org/w/index.php?title=Isotopy&diff=963&oldid=prevVipul at 00:04, 3 November 20072007-11-03T00:04:22Z<p></p>
<p><b>New page</b></p><div>==Definition==<br />
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Let <math>X</math> be a [[topological space]] and <math>f,g</math> be homeomorphisms from <math>X</math> to itself. An '''isotopy''' from <math>f</math> to <math>g</math> is a homotopy <math>F:X \times I \to X</math> that starts at <math>f</math>, ends at <math>g</math>, and such that for any fixed <math>t</math>, the map <math>x \mapsto F(x,t)</math> is a homeomorphism.<br />
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Loosely, it is a homotopy via homeomorphisms.<br />
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A composite of isotopies gives an isotopy, and hence being isotopic defines an equivalence relation on the group of all homeomorphisms. The quotient of the group of all homeoomorphisms by this equivalence relation gives the [[mapping class group]] of the topological space.</div>Vipul