ReadMeSL2

ATTENTION: You may want to skip copying the file SL2O-2 as some HAP-functions rely on a file which already has this name. For conistency's sake I kept the name.


The contractible complexes are all given in HAP-readable format. To access the information copy the files to GAP-DIRECTORY/pkg/Hap1.10/lib/Perturbations/Gcomplexes/. After loading HAP you may then use the command "ContractibleGcomplex("filename")" to construct the desired non-free resolution in GAP/HAP.

The files labeled "SL2(O-d)" contain contractible complexes for the special linear groups of degree 2 over the integers of the imaginary quadratic number field Q(sqrt(-d)).

The files labeled "SL(O-d+I)" contain contractible complexes for the special groups of module automorphisms of lattices of rank 2 over the integers of the imaginary quadratic number field Q(sqrt(-d)) with non-trivial Steinitz-class. In the case of a larger class group there are files labeled "SL(O-d+I2)",...,"SL(O-d+Ik)" and the Ij together with O-d form a system of representatives of elements of the class group modulo squares and Galois action.