chap0.txt

  
  
                             The SCO Package Manual
  
  
                       Simplicial Cohomology of Orbifolds
  
  
                               Version 2017.09.10
  
  
                                  August 2011
  
  
                                 Simon Görtzen
  
  
  
  Simon Görtzen
      Email:    mailto:[email protected]
      Homepage: http://wwwb.math.rwth-aachen.de/goertzen/
      Address:  Lehrstuhl B für Mathematik
                RWTH Aachen
                Templergraben 64
                52062 Aachen
                (Germany)
  
  
  
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  Abstract
  This document explains the primary uses of the SCO 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; [Gör08a]).
  
  
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  Copyright
  © 2007-2011 by Simon Görtzen
  
  This  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2.
  
  
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  Acknowledgements
  The SCO 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  SCO  in  its  current functionality is dependent on the GAP
  package homalg by M. Barakat [BR08], as it relies on homalg to do the actual
  computations. This manual was created with the help of the GAPDoc package by
  M. Neunhöffer and F. Lübeck.
  
  
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  Contents (SCO)
  
  1 Introduction
    1.1 Overview over this manual
    1.2 Installation of the SCO Package
  2 Usage
    2.1 The Examples Script
    2.2 Working Manually
  3 Examples
    3.1 Example 1: Klein Bottle
    3.2 Example 2: V_4
    3.3 Example 3: The "Teardrop" orbifold
  4 SCO methods and functions
    4.1 Methods and functions for orbifold triangulations
      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 Methods and functions for simplicial sets
      4.2-1 SimplicialSet
      4.2-2 SimplicialSet
      4.2-3 ComputeNextDimension
      4.2-4 Extend
    4.3 Methods and functions for matrix creation and computation
      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 An Overview of the SCO package source code