Homotopy similarity of maps. Strong similarity

Given pointed cellular spaces $X$ and $Y$, $X$ compact, and an integer $r\ge0$, we define a relation $\overset r\approx$ on $[X,Y]$ and argue for the conjecture that it always coincides with the $r$-similarity $\overset r\sim$.

💡 Research Summary

The paper introduces a new equivalence relation on the set of homotopy classes of pointed maps between cellular spaces, denoted by (a , r!\approx! b) and called strong (r)-similarity. The setting is that (X) and (Y) are pointed cellular spaces with (X) compact, and an integer (r\ge 0) is fixed. The authors build on their earlier work