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<div class="chlinktop"><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="chapA.html">A</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

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<h1>SCO</h1>


<h2>SCO - Simplicial Cohomology of Orbifolds</h2>

<p>
    2023.08-01</p>

<p>
    23 August 2023
  </p>

</div>
<p><b>
    Simon Görtzen




  </b>
<br />Email: <span class="URL"><a href="mailto:simon.goertzen@rwth-aachen.de">simon.goertzen@rwth-aachen.de</a></span>
<br />Homepage: <span class="URL"><a href="https://www.linkedin.com/in/simongoertzen/">https://www.linkedin.com/in/simongoertzen/</a></span>
<br />Address: <br />Simon Görtzen<br /> Lehrstuhl B fuer Mathematik, RWTH Aachen<br /> Templergraben 64<br /> 52062 Aachen<br /> Germany<br />
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<h3>Abstract</h3>
<p>This document explains the primary uses of the <strong class="pkg">SCO</strong> package. Included in this manual is a documented list of the most important methods and functions you will need. For the theoretical basis of this package please refer to my diploma thesis and the corresponding paper (work in progress; <a href="chapBib.html#biBGoe">[G\t08]</a>).</p>

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<h3>Copyright</h3>
<p>© 2007-2011 by Simon Goertzen</p>

<p>This package may be distributed under the terms and conditions of the GNU Public License Version 2 or (at your option) any later version.</p>

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<h3>Acknowledgements</h3>
<p>The <strong class="pkg">SCO</strong> package would not have been possible without the theoretical work by I. Moerdijk and D. A. Pronk concerning simplicial cohomology of orbifolds <a href="chapBib.html#biBmps">[MP99]</a>. Many thanks to these two, as well as Mohamed Barakat and the Lehrstuhl B für Mathematik at RWTH Aachen University in general. It should be noted that <strong class="pkg">SCO</strong> in its current functionality is dependent on the <strong class="pkg">GAP</strong> package <strong class="pkg">homalg</strong> by M. Barakat <a href="chapBib.html#biBhomalg-package">[BLH20]</a>, as it relies on <strong class="pkg">homalg</strong> to do the actual computations. This manual was created with the help of the <strong class="pkg">GAPDoc</strong> package by M. Neunhöffer and F. Lübeck.</p>

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<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X786BACDB82918A65">1.1 <span class="Heading">Overview over this manual</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X809CA9A37BE88D33">1.2 <span class="Heading">Installation of the <strong class="pkg">SCO</strong> Package</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2.html#X86A9B6F87E619FFF">2 <span class="Heading">Usage</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X79F33723829E90DB">2.1 <span class="Heading">The Examples Script</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7F193D117BD03FE3">2.2 <span class="Heading">Working Manually</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap3.html#X7A489A5D79DA9E5C">3 <span class="Heading">Examples</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X8274E5BE843F2E82">3.1 <span class="Heading">Example 1: Klein Bottle</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X80480E847C3EA8B3">3.2 <span class="Heading">Example 2: <span class="SimpleMath">V_4</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X86B3ED7B8425DCF4">3.3 <span class="Heading">Example 3: The "Teardrop" orbifold</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap4.html#X8394FA997C62A89C">4 <span class="Heading"><strong class="pkg">SCO</strong> methods and
functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X822BCAB878B669A5">4.1 <span class="Heading">Methods and functions for orbifold
triangulations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X817F45D6780F45F7">4.1-1 OrbifoldTriangulation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X79E4BB4F849AC8A1">4.1-2 Vertices</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7AC3235E8044172B">4.1-3 Simplices</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7D9F409380816CB5">4.1-4 Isotropy</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X795D2855804A5855">4.1-5 Mu</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X83926F268523C541">4.1-6 MuData</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7E845DE47C817088">4.1-7 InfoString</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7B0172DD7CD92CD8">4.2 <span class="Heading">Methods and functions for simplicial sets</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7DD68A0E7E3A4A51">4.2-1 SimplicialSet</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7DC060057E853275">4.2-2 SimplicialSet</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X80091ADD7F0D80F2">4.2-3 ComputeNextDimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7BAB245A8009088D">4.2-4 Extend</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X87335B4B8437DA4B">4.3 <span class="Heading">Methods and functions for matrix creation and
computation</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7F28FA7B83B681E8">4.3-1 BoundaryOperator</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X80C3C6867CE9FE3E">4.3-2 CreateBoundaryMatrices</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X85A9D5CB8605329C">4.3-3 Homology</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8320B03E7FEB2BA8">4.3-4 CreateCoboundaryMatrices</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X84CFC57B7E9CCCF7">4.3-5 Cohomology</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X85874A8979FF9E82">4.3-6 SCO_Examples</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapA.html#X7C5040A1817F80AC">A <span class="Heading">An Overview of the <strong class="pkg">SCO</strong> package source code</span></a>
</div>
<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
<br />
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