Calculation of Nielsen periodic numbers of fibre preserving maps

Abstract

In 2000 Heath and Keppelmann proved the naïve type addition formulae expressing the Nielsen periodic numbers NPn(f) and NFn(f) of the fibre preserving map (f,f¯) with the base map f¯n weakly Jiang, as simple sums of the Nielsen periodic numbers on the fibres. In this paper we extend these formulae to the general case. Our formulae are particularly useful for fibre preserving maps f with the base map f¯n non-weakly Jiang. We illustrate these formulae with examples of fibre preserving maps on a circle bundle over the Klein bottle.