Fixed points on model solvmanifold pairs

In this paper we define model solvmanifold pairs and their diagonal type selfmaps in the tradition of Heath and Keppelmann. We derive an explicit formula for computing the relative Nielsen number N(F;X,A)N(F;X,A) on these spaces and selfmaps F:(X,A)→(X,A)F:(X,A)→(X,A). We find that model solvmanifold pairs often exhibit interesting Schirmer theory, meaning N(F;X,A)>max{N(F),N(F|A)}N(F;X,A)>max{N(F),N(F|A)}.