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 <th style="vertical-align: top;"><big></big><big> About HAP: Table Of Contents 
 </big> </th>
 </tr>
 <tr style="color: rgb(0, 0, 102);">
 <td
style="vertical-align: top; background-color: rgb(255, 255, 255); text-align: left;">
 <ul style="font-family: helvetica,arial,sans-serif;">
 </ul>
 <div style="text-align: left;"><a href="../../index.html">HAP
Home</a></div>
 <ul style="font-family: helvetica,arial,sans-serif;">
 <li><a href="aboutIntro.html">Overview</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutDefinitions.html">Algebraic definition of
group cohomology 
 </a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutTopology.html">Topological view of group
cohomology</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutGouter.html">Extensions and second cohomology</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutBogomolov.html">Bogomolov multipliers</a> 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutCrossedMods.html">Homotopy 2-types and third
cohomology</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutSimplicialGroups.html">Homology of simplicial
groups and of 2-types</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutquasi.html">Enumerating homotopy 2-types</a> 
 </li>
 </ul>
 <big></big>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutExtensions.html">Resolutions for extensions
of groups</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutArithmetic.html">Resolutions for arithmetic
groups</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutBredon.html">Bredon homology</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutDavisComplex.html">Davis
Complex</a><a> [by Alexander Rahm & Ruben
Sanchez-Garcia] 
 </a></li>
 <a> </a>
 </ul>
 <a> </a>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <a> </a>
 <li><a href="aboutFunctorial.html">Functorial properties of
cohomology</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutCoefficientSequence.html">Exact cohomology
coefficient sequence </a> 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutSuperperfect.html">Third integral homology of
some superperfect groups 
 </a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutPeriodic.html">Second homotopy groups of
presentations and a periodic resolution for a group not acting on a
sphere</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="table/help.html">Presentations and modules of
identities for the nonabelian groups of order at most 30</a> 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutAspherical.html">Aspherical presentations</a> 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutTensorSquare.html">Third homotopy groups of
suspensions of classifying spaces</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutNonabelian.html">Nonabelian tensor product of crossed modules</a></li>
 </ul>

 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutSchurMultiplier.html">A relative Schur
multiplier, Baer invariants and the capability of groups</a></li>
 
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutArtinGroups.html">Resolutions for some
(infinite) Artin
groups</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutCoxeter.html">Resolutions for Coxeter groups</a> 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutNoncrossing.html">Non-crossing partitions for
finite Coxeter groups</a> 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutCohomologyRings.html">Cup product and
integral cohomology rings</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutModPRings.html">Mod p cohomology rings</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutPoincareSeries.html">Poincare series for
groups of order 32 
 </a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutPoincareSeriesII.html">Poincare series for
groups of order 64 
 </a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutTorAndExt.html">Tor and Ext of modules over a
mod p group ring</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutTwistedCoefficients.html">Cohomology with
twisted coefficients</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutGraphsOfGroups.html">Resolutions for graphs
of groups, Fuchsian groups and Kleinian groups 
 </a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutSpaceGroup.html">Piecing things together - a
space group example</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutRosenbergerMonster.html">Piecing things
together - the Rosenberger monster</a> 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutCocycles.html">Explicit cocycles</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutPolytopes.html">Groups acting on polytopes</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="bieberbach.html"><big
style="font-family: helvetica,arial,sans-serif;">Betti numbers
for some orientable 7-</big></a><big><a
href="bieberbach.html">dimensional Hantzsche-Wendt Manifolds</a>
(using HAPcryst) 
 </big></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="3dflatmanifolds.html">Fundamental domains for
3-dimensional flat manifolds</a> (using HAPcryst) 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutLie.html">On a relationship between group
homology and Lie algebra homology</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutLieCovers.html">Lie covering homomorphisms</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="AboutTorsionSubcomplexes.html">Torsion subcomplexes</a>
[by Alexander Rahm and Bui Anh Tuan] 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutCubical.html">Simplicial, cubical,
permutahedral and regular
CW-complexes</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutRandomComplexes.html">Random simplicial
complexes</a> 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutLinks.html">The fundamental group of
CW-complexes</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutKnots.html">Knots, links and proteins</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutPeripheral.html">Computing a peripheral
system for a 3-manifold</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutCoverinSpaces.html">Covering spaces</a> 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutQuandles.html">Quandles</a> 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutPersistent.html">Persistent homology</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutMetrics.html">Metric Spaces</a> 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutTDA.html">Digital image analysis</a> 
 </li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutParallel.html">Parallel computation</a></li>
 </ul>
 <ul
style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutAbelianCategories.html">Programming
homological diagrams in abelian categories 
 </a></li>
 </ul>
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style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);">
 <li><a href="aboutPerformance.html">Computational performance
of HAP</a></li>
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