Abstract

The Nielsen number for n-valued multimaps, defined by Schirmer, has been calculated only for the circle. A concept of n-valued fiber map on the total space of a fibration is introduced. A formula for the Nielsen numbers of n-valued fiber maps of fibrations over the circle reduces the calculation to the computation of Nielsen numbers of single-valued maps. If the fibration is orientable, the product formula for single-valued fiber maps fails to generalize, but a “semi-product formula ” is obtained. In this way, the class of n-valued multimaps for which the Nielsen number can be computed is substantially enlarged. Subject Classification 55M20, 54C60 1

Citations