|
|
|
|
SSL chap30_mj.html
Sprache: HTML
|
|
| products/Sources/formale Sprachen/GAP/pkg/hap/doc/chap30_mj.html |
 |
<?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>
<script type="text/javascript"
src="https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<title>GAP (HAP commands) - Chapter 30: Regular CW-Complexes</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" />
<script src="manual.js" type="text/javascript"></script>
<script type="text/javascript">overwriteStyle();</script>
</head>
<body class="chap30" onload="jscontent()">
<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a> <a href="chap1_mj.html">1</a> <a href="chap2_mj.html">2</a> <a href="chap3_mj.html">3</a> <a href="chap4_mj.html">4</a> <a href="chap5_mj.html">5</a> <a href="chap6_mj.html">6</a> <a href="chap7_mj.html">7</a> <a href="chap8_mj.html">8</a> <a href="chap9_mj.html">9</a> <a href="chap10_mj.html">10</a> <a href="chap11_mj.html">11</a> <a href="chap12_mj.html">12</a> <a href="chap13_mj.html">13</a> <a href="chap14_mj.html">14</a> <a href="chap15_mj.html">15</a> <a href="chap16_mj.html">16</a> <a href="chap17_mj.html">17</a> <a href="chap18_mj.html">18</a> <a href="chap19_mj.html">19</a> <a href="chap20_mj.html">20</a> <a href="chap21_mj.html">21</a> <a href="chap22_mj.html">22</a> <a href="chap23_mj.html">23</a> <a href="chap24_mj.html">24</a> <a href="chap25_mj.html">25</a> <a href="chap26_mj.html">26</a> <a href="chap27_mj.html">27</a> <a href="chap28_mj.html">28</a> <a href="chap29_mj.html">29</a> <a href="chap30_mj.html">30</a> <a href="chap31_mj.html">31</a> <a href="chap32_mj.html">32</a> <a href="chap33_mj.html">33</a> <a href="chap34_mj.html">34</a> <a href="chap35_mj.html">35</a> <a href="chap36_mj.html">36</a> <a href="chap37_mj.html">37</a> <a href="chap38_mj.html">38</a> <a href="chap39_mj.html">39</a> <a href="chap40_mj.html">40</a> <a href="chapInd_mj.html">Ind</a> </div>
<div class="chlinkprevnexttop"> <a href="chap0_mj.html">[Top of Book]</a> <a href="chap0_mj.html#contents">[Contents]</a> <a href="chap29_mj.html">[Previous Chapter]</a> <a href="chap31_mj.html">[Next Chapter]</a> </div>
<p id="mathjaxlink" class="pcenter"><a href="chap30.html">[MathJax off]</a></p>
<p><a id="X855CD0808058727D" name="X855CD0808058727D"></a></p>
<div class="ChapSects"><a href="chap30_mj.html#X855CD0808058727D">30 <span class="Heading">Regular CW-Complexes</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap30_mj.html#X7CFDEEC07F15CF82">30.1 <span class="Heading"> </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap30_mj.html#X825EF11A86624E44">30.1-1 SimplicialComplexToRegularCWComplex</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap30_mj.html#X8723DF8A7AA8AE9E">30.1-2 CubicalComplexToRegularCWComplex</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap30_mj.html#X802E1927807969C1">30.1-3 CriticalCellsOfRegularCWComplex</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap30_mj.html#X7A1C427578108B7E">30.1-4 ChainComplex</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap30_mj.html#X8307D5A57EFAC8EE">30.1-5 ChainComplexOfRegularCWComplex</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap30_mj.html#X7EAE7E4181546C17">30.1-6 FundamentalGroup</a></span>
</div></div>
</div>
<h3>30 <span class="Heading">Regular CW-Complexes</span></h3>
<p><a id="X7CFDEEC07F15CF82" name="X7CFDEEC07F15CF82"></a></p>
<h4>30.1 <span class="Heading"> </span></h4>
<p><a id="X825EF11A86624E44" name="X825EF11A86624E44"></a></p>
<h5>30.1-1 SimplicialComplexToRegularCWComplex</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SimplicialComplexToRegularCWComplex</code>( <var class="Arg">K</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a simplicial complex <span class="SimpleMath">\(K\)</span> and returns the corresponding regular CW-complex.</p>
<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutMetrics.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutRandomComplexes.html">2</a></span> </p>
<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">‣ CubicalComplexToRegularCWComplex</code>( <var class="Arg">K</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">‣ CubicalComplexToRegularCWComplex</code>( <var class="Arg">K</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 <span class="SimpleMath">\(K\)</span> is returned.</p>
<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><td class="tdright">( function )</td></tr></table></div>
<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> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a regular CW-complex <span class="SimpleMath">\(Y\)</span> and returns the critical cells of <span class="SimpleMath">\(Y\)</span> with respect to some discrete vector field. If <span class="SimpleMath">\(Y\)</span> does not initially have a discrete vector field then one is constructed.</p>
<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">\(CriticalCellsOfRegularCWComplex(Y)\)</span> works by homotopy reducing cells starting at the top dimension. The function <span class="SimpleMath">\(CriticalCellsOfRegularCWComplex(Y,n)\)</span> works by homotopy coreducing cells starting at dimension 0. The two methods may well return different numbers of cells.</p>
<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutPeripheral.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutRandomComplexes.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnots.html">3</a></span> </p>
<p><a id="X7A1C427578108B7E" name="X7A1C427578108B7E"></a></p>
<h5>30.1-4 ChainComplex</h5>
<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 )</td></tr></table></div>
<p>Inputs a regular CW-complex <span class="SimpleMath">\(Y\)</span> and returns the cellular chain complex of a CW-complex W whose cells correspond to the critical cells of <span class="SimpleMath">\(Y\)</span> with respect to some discrete vector field. 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/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>
<p>Inputs a regular CW-complex <span class="SimpleMath">\(Y\)</span> and returns the cellular chain complex of <span class="SimpleMath">\(Y\)</span>.</p>
<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">12</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutKnots.html">13</a></span> </p>
<div class="chlinkprevnextbot"> <a href="chap0_mj.html">[Top of Book]</a> <a href="chap0_mj.html#contents">[Contents]</a> <a href="chap29_mj.html">[Previous Chapter]</a> <a href="chap31_mj.html">[Next Chapter]</a> </div>
<div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a> <a href="chap1_mj.html">1</a> <a href="chap2_mj.html">2</a> <a href="chap3_mj.html">3</a> <a href="chap4_mj.html">4</a> <a href="chap5_mj.html">5</a> <a href="chap6_mj.html">6</a> <a href="chap7_mj.html">7</a> <a href="chap8_mj.html">8</a> <a href="chap9_mj.html">9</a> <a href="chap10_mj.html">10</a> <a href="chap11_mj.html">11</a> <a href="chap12_mj.html">12</a> <a href="chap13_mj.html">13</a> <a href="chap14_mj.html">14</a> <a href="chap15_mj.html">15</a> <a href="chap16_mj.html">16</a> <a href="chap17_mj.html">17</a> <a href="chap18_mj.html">18</a> <a href="chap19_mj.html">19</a> <a href="chap20_mj.html">20</a> <a href="chap21_mj.html">21</a> <a href="chap22_mj.html">22</a> <a href="chap23_mj.html">23</a> <a href="chap24_mj.html">24</a> <a href="chap25_mj.html">25</a> <a href="chap26_mj.html">26</a> <a href="chap27_mj.html">27</a> <a href="chap28_mj.html">28</a> <a href="chap29_mj.html">29</a> <a href="chap30_mj.html">30</a> <a href="chap31_mj.html">31</a> <a href="chap32_mj.html">32</a> <a href="chap33_mj.html">33</a> <a href="chap34_mj.html">34</a> <a href="chap35_mj.html">35</a> <a href="chap36_mj.html">36</a> <a href="chap37_mj.html">37</a> <a href="chap38_mj.html">38</a> <a href="chap39_mj.html">39</a> <a href="chap40_mj.html">40</a> <a href="chapInd_mj.html">Ind</a> </div>
<hr />
<p class="foot">generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>
</body>
</html>
¤ Dauer der Verarbeitung: 0.30 Sekunden
(vorverarbeitet)
¤
*© Formatika GbR, Deutschland
|
|
2026-03-28
|
|
|
|
|
