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<p>For an <i>n</i>-valued self-map <i>f</i> of a closed manifold <i>X</i>,&#xa0; we prove an averaging formula for the Reidemeister trace of <i>f</i> in terms of the Reidemeister coincidence traces of single-valued maps between finite orientable covering spaces of <i>X</i>. We then derive analogous formulas for the Lefschetz and Nielsen numbers of <i>f</i>. In the special case where <i>X</i> is an infra-nilmanifold, we obtain explicit formulas for the Lefschetz and Nielsen numbers of any <i>n</i>-valued map on <i>X</i>.</p>

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Averaging formulas for the Reidemeister trace, Lefschetz and Nielsen numbers of n-valued maps

  • 期刊论文

  • 发表日期：

    2025年4月15日

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  • Karel Dekimpe,
  • Lore De Weerdt

摘要

For an n-valued self-map f of a closed manifold X,  we prove an averaging formula for the Reidemeister trace of f in terms of the Reidemeister coincidence traces of single-valued maps between finite orientable covering spaces of X. We then derive analogous formulas for the Lefschetz and Nielsen numbers of f. In the special case where X is an infra-nilmanifold, we obtain explicit formulas for the Lefschetz and Nielsen numbers of any n-valued map on X.