About HAP: Table Of Contents
HAP Home Introduction Algebraic definition of group cohomology Topological view of group cohomology Extensions and second cohomology Homotopy 2-types and third cohomology Resolutions for extensions of groups Functorial properties of cohomology Third integral homology of some superperfect groups Second homotopy groups of presentations and a periodic resolution for a group not acting on a sphere Presentations and modules of identities for the nonabelian groups of order at most 30 Aspherical presentations Third homotopy groups of suspensions of classifying spaces A relative Schur multiplier, Baer invariants and the capability of groups Resolutions for some infinite (Artin) groups Non-crossing partitions for finite Coxeter groups Cup product and integral cohomology rings Mod p cohomology rings Poincare series for groups of order 32 Poincare series for groups of order 64 Tor and Ext of modules over a mod p group ring Cohomology with twisted coefficients Resolutions for graphs of groups, Fuchsian groups and Kleinian groups Piecing things together - a space group example Piecing things together - the Rosenberger monster Explicit cocycles Groups acting on polytopes Betti numbers for some orientable 7-dimensional Hantzsche-Wendt Manifolds (using HAPcryst) Fundamental domains for 3-dimensional flat manifolds (using HAPcryst) On a relationship between group homology and Lie algebra homology Lie covering homomorphisms Topological data analysis Parallel computation Programming homological diagrams in abelian categories Computational performance of HAP Future work: Implement contracting homotopies for the function ResolutionArtinGroup() . Develop more functions for "ZG-resolutions with non-free G-action". Such a resolution R is similar to a free resolution except that it has a component R.stabilizer(e) which returns the stabilizer subgroup Ge in G of each generator e of R. We need to implement a function MakeFree(R) which, using the non-free resolution R and free resolutions Re for each stabilizer group, constructs a free ZG-resolution. The algorithm is explained in [G. Ellis, J. Harris & E. Sköldberg, "Polytopal resolutions for finite groups", J. Reine Angewandte Math., to appear]. Apply the function MakeFree(R) in the construction of free ZG-resolutions for: (1) Coxeter groups G which act on the so-called Davis complex; (2) some infinite generalised triangle groups G which act on hyperbolic 3-space; finite groups G acting faithfully on Euclidean space (this will use Polymake software). HAP Home