Homotopy similarity of maps. Compositions

TL;DR

This paper investigates how homotopy similarity relations and finite-order invariants behave under induced maps, especially when the map is strongly similar to a constant, providing insights into their structural properties.

Contribution

It characterizes the behavior of homotopy similarity and invariants under specific induced maps that are strongly similar to constant maps.

Findings

Homotopy similarity relations are preserved under certain induced maps.

Finite-order invariants exhibit specific transformation properties under these maps.

The results deepen understanding of homotopy invariants in relation to strongly similar maps.

Abstract

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 constant map.