Abstract
This is my old unpublished paper called "The generalized Grassmann invariant". It shows how "pictures" also known as "Peiffer diagrams" represent elements of H3G for any group G and shows that K3(Z [G]) is isomorphic to a group of deformation classes of pictures for the Steinberg group of Z[G]. A picture representing an element of order 16 in K3(Z)= Z48 is also constructed. In this updated version of the paper, we modify only the pictures and leave the text more or less unchanged. We also added an Appendix to explain the new pictures using representations of quivers and root systems of type An. Often, some roots are missing in the Morse pictures. We give two ideas to replace these roots. One uses "ghost handle slides" to obtain a standard picture. The second idea uses the (real) Cartan subalgebra H to obtain a "relative" picture for a torsion class and adds "ghost modules" which are directly related to the generalized Grassmann invariant. Additions and changes are in blue except the pictures are black with colored ghosts.