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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta http-equiv="content-type" content="text/html; charset=ISO-8859-1"> <title>AboutHap</title> </head> <body style="color: rgb(0, 0, 153); background-color: rgb(204, 255, 255);" link="#000066" vlink="#000066" alink="#000066"> <br> <table style="text-align: left; margin-left: auto; margin-right: auto; color: rgb(0, 0, border="0" cellpadding="20" cellspacing="10"> <tbody> <tr align="center"> <th style="vertical-align: top;"><big><span style="font-weight: bold;"></span></big><big><span style="font-weight: bold;"><span style="font-family: opensymbol;"> <span style="font-family: opensymbol;"></span></span></span><span style="font-weight: bold;">About HAP: Table Of Contents<br> </span></big> </th> </tr> <tr style="color: rgb(0, 0, 102);"> <td style="vertical-align: top; background-color: rgb(255, 255, 255); text-align: le <ul style="font-family: helvetica,arial,sans-serif;"> </ul> <div style="text-align: left;"><a href="../../index.html"><small>HAP Home</small></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<br> </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><br> </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><span style="font-weight: bold;"><br> </span></li> </ul> <big><span style="font-weight: bold;"></span></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]<br> </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><br> </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<br> </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><br> </li> </ul> <ul style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);"> <li><a href="aboutAspherical.html">Aspherical presentations</a><br> </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> <small> </small> </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><br> </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><br> </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<br> </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<br> </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<br> </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><br> </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;"><small>Betti numbers for some orientable 7-</small></big></a><big><small style="font-family: helvetica,arial,sans-serif;"><a href="bieberbach.html">dimensional Hantzsche-Wendt Manifolds</a> (using HAPcryst)<br> </small></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)<br> </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]<br> </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><br> </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><br> </li> </ul> <ul style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);"> <li><a href="aboutQuandles.html">Quandles</a> <br> </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><br> </li> </ul> <ul style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);"> <li><a href="aboutTDA.html">Digital image analysis</a><br> </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<br> </a></li> </ul> <ul style="font-family: helvetica,arial,sans-serif; color: rgb(0, 0, 102);"> <li><a href="aboutPerformance.html">Computational performance of HAP</a></li> </ul> <br> <span style="font-family: helvetica,arial,sans-serif;"></span><br> <a href="../../index.html">HAP Home</a><br> <ul> </ul> </td> </tr> </tbody> </table> <br> <br> </body> </html>
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2026-04-02