  
  
                                     [1X SCO [101X
  
  
                   [1X SCO - Simplicial Cohomology of Orbifolds [101X
  
  
                                   2022.09-01
  
  
                                7 September 2022
  
  
                                 Simon Görtzen
  
  
  
  Simon Görtzen
      Email:    [7Xmailto:simon.goertzen@rwth-aachen.de[107X
      Homepage: [7Xhttps://www.linkedin.com/in/simongoertzen/[107X
      Address:  [33X[0;14YSimon Görtzen[133X
                [33X[0;14YLehrstuhl B fuer Mathematik, RWTH Aachen[133X
                [33X[0;14YTemplergraben 64[133X
                [33X[0;14Y52062 Aachen[133X
                [33X[0;14YGermany[133X
  
  
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThis document explains the primary uses of the [5XSCO[105X 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; [G\t08]).[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2007-2011 by Simon Goertzen[133X
  
  [33X[0;0YThis  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2 or (at your option) any later version.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YThe [5XSCO[105X package would not have been possible without the theoretical work by
  I.  Moerdijk  and  D. A. Pronk concerning simplicial cohomology of orbifolds
  [MP99].  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  [5XSCO[105X  in  its  current functionality is dependent on the [5XGAP[105X
  package  [5Xhomalg[105X  by  M.  Barakat  [BLH20],  as it relies on [5Xhomalg[105X to do the
  actual  computations.  This  manual  was created with the help of the [5XGAPDoc[105X
  package by M. Neunhöffer and F. Lübeck.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (SCO)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YOverview over this manual[133X
    1.2 [33X[0;0YInstallation of the [5XSCO[105X Package[133X
  2 [33X[0;0YUsage[133X
    2.1 [33X[0;0YThe Examples Script[133X
    2.2 [33X[0;0YWorking Manually[133X
  3 [33X[0;0YExamples[133X
    3.1 [33X[0;0YExample 1: Klein Bottle[133X
    3.2 [33X[0;0YExample 2: [22XV_4[122X[133X
    3.3 [33X[0;0YExample 3: The "Teardrop" orbifold[133X
  4 [33X[0;0Y[5XSCO[105X methods and functions[133X
    4.1 [33X[0;0YMethods and functions for orbifold triangulations[133X
      4.1-1 OrbifoldTriangulation
      4.1-2 Vertices
      4.1-3 Simplices
      4.1-4 Isotropy
      4.1-5 Mu
      4.1-6 MuData
      4.1-7 InfoString
    4.2 [33X[0;0YMethods and functions for simplicial sets[133X
      4.2-1 SimplicialSet
      4.2-2 SimplicialSet
      4.2-3 ComputeNextDimension
      4.2-4 Extend
    4.3 [33X[0;0YMethods and functions for matrix creation and computation[133X
      4.3-1 BoundaryOperator
      4.3-2 CreateBoundaryMatrices
      4.3-3 Homology
      4.3-4 CreateCoboundaryMatrices
      4.3-5 Cohomology
      4.3-6 SCO_Examples
  A [33X[0;0YAn Overview of the [5XSCO[105X package source code[133X
  
  
  [32X
