<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head> <title>GAP (HAP) - Chapter 3: Induced equivariant chain maps</title> <meta http-equiv="content-type" content="text/html; charset=UTF-8" /> <meta name="generator" content="GAPDoc2HTML" /> <link rel="stylesheet" type="text/css" href="manual.css" /> </head> <body><a href="../www/index.html"><small>HAP home</small></a> <div class="chlinkprevnexttop"> <a href="chap0.html">Top of Book</a> <a href="chap2.html">Previous Chapter</a> <a href="chap4.html">Next Chapter</a> </div> <p><a id="X7E91068780486C3A" name="X7E91068780486C3A"></a></p> <div class="ChapSects"><a href="chap3.html#X7E91068780486C3A">3. <span class="Heading"> Induced equivariant chain maps</span></a> </div> <h3>3. <span class="Heading"> Induced equivariant chain maps</span></h3> <div class="pcenter"><table cellspacing="10" class="GAPDocTable"> <tr> <td class="tdleft"><code class="code"> EquivariantChainMap(R,S,f)</code></p> <p>Inputs a ZG-resolution R, a ZG'-resolution S, and a group homomorphism f : G --> G'. It outputs a component object M with the following components.</p> <ul> <li><p>M!.source is the resolution R.</p> </li> <li><p>M!.target is the resolution S.</p> </li> <li><p>M!.mapping(w,n) is a function which gives the image in S_n, under a chain map induced by f, of a word w in R_n. (Here R_n and S_n are the n-th modules in the resolutions R and S.)</p> </li> <li><p>F!.properties is a list of pairs such as ["type", "equivariantChainMap"].</p> </li> </ul> <p>The resolution S must have a contracting homotopy.</td> </tr> </table><br /><p> </p><br /> </div> <div class="chlinkprevnextbot"> <a href="chap0.html">Top of Book</a> <a href="chap2.html">Previous Chapter</a> <a href="chap4.html">Next Chapter</a> </div> <div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a href="chap1.html">1</a> <a href="chap2.html">2</a> <a href="chap3.html">3</a> <a href="chap4.html">4</a> <a href="chap5.html">5</a> <a href="chap6.html">6</a> <a href="chap7.html">7</a> <a href="chap8.html">8</a> <a href="chap9.html">9</a> <a href="chap10.html">10</a> <a href="chap11.html">11</a> <a href="chap12.html">12</a> <a href="chap13.html">13</a> <a href="chap14.html">14</a> <a href="chap15.html">15</a> <a href="chap16.html">16</a> <a href="chap17.html">17</a> <a href="chap18.html">18</a> <a href="chap19.html">19</a> <a href="chap20.html">20</a> <a href="chap21.html">21</a> <a href="chap22.html">22</a> <a href="chap23.html">23</a> <a href="chap24.html">24</a> <a href="chap25.html">25</a> <a href="chapInd.html">Ind</a> </div> <hr /> <p class="foot">generated by <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p> </body> </html>