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.
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Dedicated, with gratitude, to Felix Browder who, long ago, encouraged and supported a young topologist’s interest in fixed point theory
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Brown, R.F. Nielsen numbers of n-valued fiber maps. J. fixed point theory appl. 4, 183–201 (2008). https://doi.org/10.1007/s11784-008-0098-x
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DOI: https://doi.org/10.1007/s11784-008-0098-x