S. Podkorytov

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math.AT2026

Homotopy similarity of maps. Strong similarity

S. S. Podkorytov

Given pointed cellular spaces $X$ and $Y$ , $X$ compact, and an integer $r \geq 0$ , we define a relation $\approx r$ on $[X, Y]$ and argue for the conjecture that it always coin…

math.AT2026

Homotopy similarity of maps. Maps of the circle

S. S. Podkorytov

We describe the relation of $r$ -similarity and finite-order invariants on the homotopy set $[S^{1}, Y] = I ¨ _{1} (Y)$ .

math.AT2026

Homotopy similarity of maps. Compositions

S. S. Podkorytov

We describe the behaviour of the homotopy similarity relations and finite-order invariants under the function $[X, Y] \to [X, Z]$ induced by a map $Y \to Z$ strongly $r$ -similar to the…

math.AT2024

Homotopy similarity of maps

S. S. Podkorytov

Given based cellular spaces X and Y, X compact, we define a sequence of increasingly fine equivalences on the based-homotopy set [X,Y].