AboutHap

About HAP: Table Of Contents
Introduction Algebraic definition of group cohomology Topological view of group 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 Cup product and integral cohomology rings Mod p cohomology rings 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 On a relationship between group homology and Lie algebra homology Computational performance of HAP Future work: Implement contracting homotopies for the function ResolutionArtinGroup() . Implement functions for the abelian extensions of groups which are classified by second cohomology. It might also be worth implementing Mac Lanes's third cohomology obstruction to the existence of nonabelian extensions. 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 main page