<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AutomorphismGroupAsCatOneGroup</code>( <var class="Arg">G</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a group <span class="SimpleMath">\(G\)</span> and returns the Cat-1-group <span class="SimpleMath">\(C\)</span> corresponding to the crossed module <span class="SimpleMath">\(G\rightarrow Aut(G)\)</span>.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ HomotopyGroup</code>( <var class="Arg">C</var>, <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a cat-1-group <span class="SimpleMath">\(C\)</span> and an integer n. It returns the <span class="SimpleMath">\(n\)</span>th homotopy group of <span class="SimpleMath">\(C\)</span>.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ HomotopyModule</code>( <var class="Arg">C</var>, <var class="Arg">2</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a cat-1-group <span class="SimpleMath">\(C\)</span> and an integer n=2. It returns the second homotopy group of <span class="SimpleMath">\(C\)</span> as a G-module (i.e. abelian G-outer group) where G is the fundamental group of C.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ QuasiIsomorph</code>( <var class="Arg">C</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a cat-1-group <span class="SimpleMath">\(C\)</span> and returns a cat-1-group <span class="SimpleMath">\(D\)</span> for which there exists some homomorphism <span class="SimpleMath">\(C\rightarrow D\)</span> that induces isomorphisms on homotopy groups.</p>
<p>This function was implemented by <strong class="button">Le Van Luyen</strong>.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ModuleAsCatOneGroup</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>Inputs a group <span class="SimpleMath">\(G\)</span>, an abelian group <span class="SimpleMath">\(M\)</span> and a homomorphism <span class="SimpleMath">\(\alpha\colon G\rightarrow Aut(M)\)</span>. It returns the Cat-1-group <span class="SimpleMath">\(C\)</span> corresponding th the zero crossed module <span class="SimpleMath">\(0\colon M\rightarrow G\)</span>.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MooreComplex</code>( <var class="Arg">C</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a cat-1-group <span class="SimpleMath">\(C\)</span> and returns its Moore complex as a G-complex (i.e. as a complex of groups considered as 1-outer groups).</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ XmodToHAP</code>( <var class="Arg">C</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a cat-1-group <span class="SimpleMath">\(C\)</span> obtained from the Xmod package and returns a cat-1-group <span class="SimpleMath">\(D\)</span> for which IsHapCatOneGroup(D) returns true.</p>
<p>It returns "fail" id <span class="SimpleMath">\(C\)</span> has not been produced by the Xmod package.</p>
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
