Free Crossed Resolutions of Groups and Presentations of Modules of Identities among Relations

Abstract

AbstractThe paper gives formulae for a module presentation of the module of identities among relations for a presentation of a group, in terms of information on 0- and 1-combings of the Cayley graph. These formulae are seen as a special case of formulae for extending a partial free crossed resolution of a group, given a partial contracting homotopy of the universal cover of the partial resolution.