Periodic points of self-maps of products of lens spaces $L(3)\times L(3)$
DOI:
https://doi.org/10.12775/TMNA.2022.053Keywords
Periodic points, Nielsen number, fixed point index, smooth maps, lens spaceAbstract
Let $f\colon M\to M$ be a self-map of a compact manifold and $n\in \mathbb{N}$. The least number of $n$-periodic points in the smooth homotopy class of $f$ may be smaller than in the continuous homotopy class. We ask: for which self-maps $f\colon M\to M$ the two minima are the same, for each prescribed multiplicity? In the study of self-maps of tori and compact Lie groups a necessary condition appears. Here we give a criterion which helps to decide whether the necessary condition is also sufficient. We apply this result to show that for self-maps of the product of the lens space $M=L(3)\times L(3)$ the necessary condition is also sufficient.References
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