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<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CriticalCellsOfRegularCWComplex</code>( <var class="Arg">Y</var>, <var class="Arg">n</var>
<p>Inputs a regular CW-complex <span class="SimpleMath">\(Y\)</span> and returns the critical cells of <span class="SimpleMath">\(Y\)</java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p>If a positive integer <span class="SimpleMath">\(n\)</span> is given as a second optional input, then just the critical cells in dimensions up to and including <span class="SimpleMath">\(n\)</span> are returned.</p>

<p>The function <span class="SimpleMath">\(CriticalCellsOfRegularCWComplex

<<p

<p><a id="X7A1C427578108B7E" name="X7A1C427578108B7E"></a></p>

<h5>30.1-4 ChainComplex</h5p> a regular <span="">(\<span> and returns cellular complex acorrespond the  of class"SimpleMath">\Y)/> with tosome have  then constructed/

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ChainComplex</code>( <var class="Arg">Y</var> )</td><td class="tdright">( function
pInputs CW-complexspanclass=SimpleMath>(\</pan> returns cellular complexofCW-complexW whose correspond the criticalcells <spanclass"SimpleMath"\Y\<span with vector. If< class"SimpleMath">\(Y\)</> does initiallyhavead vector fieldthen one  constructed.<>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap1.html">1</a></span> , <span class="URL"><a href="../tutorial/chap3.html">2</a></span> , <span class="URL"><a href="../tutorial/chap4.html">3</a></span> , <span class="URL"><a href="../tutorial/chap10.html">4</a></span> , <span class="URL"><a href="../tutorial/chap12.html">5</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutMetrics.html">6</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutBredon.html">7</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPersistent.html">8</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoveringSpaces.html">9</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoverinSpaces.html">10</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCubical.html">11</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutSimplicialGroups.html">12</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutIntro.html">13</a></span> </p>

<p><a id="X8307D5A57EFAC8EE" name="X8307D5A57EFAC8EE"></a></p>

<h5>30.1-5 ChainComplexOfRegularCWComplex</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ChainComplexOfRegularCWComplex</code>( <var class="Arg">Y</var> )</td><td class="tdright">( function )</td></tr></table></div<> a  CW-complex class""\(\<spanand,the ofsome-. Itreturns fundamentalgroup < classSimpleMath"\\)\(n\)/>.Thegroupis returnedas a presented group. ">(n)span specifiedthen is set \(n/span> requires discretevector fieldon< class""\Y)/pan. span=SimpleMath\Y)/> does notinitiallyhavea vector then oneisconstructed
pInputsa egular CW-complex<pan="SimpleMath>\Y\\)/span andreturns cellular chaincomplex of \(Y\).



<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap1.html">1</a></span> , <span class="URL"><a href="../tutorial/chap10.html">2</a></span> </p>

<p><a id="X7EAE7E4181546C17" name="X7EAE7E4181546C17"></a></p>

<h5>30.1-6 FundamentalGroup</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FundamentalGroup</code>( <var class="Arg">Y</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FundamentalGroup</code>( <var class="Arg">Y</var>, <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a regular CW-complex <span class="SimpleMath">\(Y\)</span> and, optionally, the number of some 0-cell. It returns the fundamental group of <span class="SimpleMath">\(Y\)</span> based at the 0-cell <span class="SimpleMath">\(n\)</span>. The group is returned as a finitely presented group. If <span class="SimpleMath">\(n\)</span> is not specified then it is set <span class="SimpleMath">\(n=1\)</span>. The algorithm requires a discrete vector field on <span class="SimpleMath">\(Y\)</span>. If <span class="SimpleMath">\(Y\)</span> does not initially have a discrete vector field then one is constructed.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap1.html">1</a></span> , <span class="URL"><a href="../tutorial/chap2.html">2</a></span> , <span class="URL"><a href="../tutorial/chap3.html">3</a></span> , <span class="URL"><a href="../tutorial/chap4.html">4</a></span> , <span class="URL"><a href="../tutorial/chap5.html">5</a></span> , <span class="URL"><a href="../tutorial/chap11.html">6</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutLinks.html">7</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPeripheral.html">8</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoveringSpaces.html">9</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoverinSpaces.html">10</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">11</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutRandomComplexes.html">1


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<div class="ChapSects"><a href="chap30_mj.html#X855CD0808058727D">30 <span class="Heading">Regular CW-Complexes</span></a>
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<h3>3

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<>31 span"


<pInputs complexspan=SimpleMath<span  the regular<pjava.lang.StringIndexOutOfBoundsException: Index 122 out of bounds for length 122

<h5>30.1-1 SimplicialComplexToRegularCWComplex</h5>

<div class="func"><table class="func" width
<p>Inputs a simplicial complex

<p><strong class="button">Examples:</strong> <span class="URL"><a href

<p><a id="X8723DF8A7AA8AE9E" name="X8723DF8A7AA8AE9E"></a></p>

<h5>30.1-2 CubicalComplexToRegularCWComplex</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">Rdiv=an style='color:blue'>""
>table=" width"1%>< =tdleft="&82; K, n/var> )> </code>( <arclassArgK</var>, <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a pure cubical complex (or cubical complex) <span class="SimpleMath">\(K\)</span> and returns the corresponding regular CW-complex. If a positive integer <span class="SimpleMath">\(n\)</span> is entered as an optional second argument, then just the <span class="SimpleMath">\(n\)</span>-skeleton of

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutKnots.html">1</a></span> </p>

<p><a id="X802E1927807969C1" name="X802E1927807969C1"></a></p>

<h5>30.1-3 CriticalCellsOfRegularCWComplex</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CriticalCellsOfRegularCWComplex</code>( <var class="Arg">Y</var> )</td><div=""> =func=0%<>< ="tdleft>class">#27 riticalCellsOfRegularCWComplex> var =""Y/varvar="">n/> )/td<dclass"&functionnbsp;<