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<div class="ChapSects"><a href="chap7.html#X7E91068780486C3A">7 <span class="Heading"> Induced equivariant chain maps</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X7CFDEEC07F15CF82">7.1 <span class="Heading"> </span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X868E2A04832619C5">7.1-1 EquivariantChainMap</a></span>
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<h3>7 <span class="Heading"> Induced equivariant chain maps</span></h3>
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<h4>7.1 <span class="Heading"> </span></h4>
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<h5>7.1-1 EquivariantChainMap</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ EquivariantChainMap</code>( <var class="Arg">R</var>, <var class="Arg">S</var>, <var class="Arg">f</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">R</span>, a <span class="SimpleMath">ZG'</span>-resolution <span class="SimpleMath">S</span>, and a group homomorphism <span class="SimpleMath">f : G ⟶ G'</span>. It outputs a component object <span class="SimpleMath">M</span> with the following components.</p>
<ul>
<li><p><span class="SimpleMath">M!.source</span> is the resolution <span class="SimpleMath">R</span>.</p>
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<li><p><span class="SimpleMath">M!.target</span> is the resolution <span class="SimpleMath">S</span>.</p>
</li>
<li><p><span class="SimpleMath">M!.mapping(w,n)</span> is a function which gives the image in <span class="SimpleMath">S_n</span>, under a chain map induced by <span class="SimpleMath">f</span>, of a word <span class="SimpleMath">w</span> in <span class="SimpleMath">R_n</span>. (Here <span class="SimpleMath">R_n</span> and <span class="SimpleMath">S_n</span> are the <span class="SimpleMath">n</span>-th modules in the resolutions <span class="SimpleMath">R</span> and <span class="SimpleMath">S</span>.)</p>
</li>
<li><p><span class="SimpleMath">F!.properties</span> is a list of pairs such as ["type", "equivariantChainMap"].</p>
</li>
</ul>
<p>The resolution <span class="SimpleMath">S</span> must have a contracting homotopy.</p>
<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap7.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCohomologyRings.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPoincareSeries.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutFunctorial.html">4</a></span> </p>
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