Nielsen fixed-point theory

Summary

Nielsen fixed-point theory studies the least number of fixed points among all maps homotopic to a given self-map $f$ of a space. It sorts the fixed points of $f$ into classes, using paths and their images, and counts the classes that cannot be removed by a homotopy. This count is the Nielsen number $N(f)$. It is a homotopy invariant and a lower bound for the number of fixed points of every map homotopic to $f$. It refines the Lefschetz number, which can only show that at least one fixed point exists.