Quasar-galaxy associations with discordant redshifts as a topological effect. I. Two-dimensional study

A previously advanced conjecture is developed that may eventually solve the quasar redshift controversy in a constructive fashion. The claimed galaxy-quasar and other associations with disordant redshifts are recognized as such, but on the level of a little-known possibility; that each associated group is the multiple image of a single source, produced by rays emitted along paths of different lengths. This is allowed by the multiply-connected topologies of Friedman's closed models of negative spatial curvature. The distances indicated by the cosmological interpretation of the redshifts are now seen as image distances, only one of them being the source's separation from us. In this first part of a two-paper sequence I deal with the problem in the relatively simple context of a hyperbolic two-dimensional space. This is physically unrealistic, but leads to a few qualitative observational suggestions; and it permits the introduction of the needed mathematical machinery, centered on the tesselations of hyperbolic spaces, in a visualizable way. Thus the reader will be prepared for the less intuitive three-dimensional research, which is outlined in the last section and will be elaborated in Part II. Some related theoretical topics are discussed. They include reinterpretations of the cosmic isotropy and of the homogeneity principle, and hints of an argumentation for the assumed closure of space