Homotopy similarity of maps. Maps of the circle

TL;DR

This paper explores the relationship between r-similarity and finite-order invariants within the homotopy set of maps from the circle, providing insights into their algebraic and topological properties.

Contribution

It establishes a connection between r-similarity and finite-order invariants in the context of maps from the circle, advancing understanding of homotopy classifications.

Findings

r-similarity relates to finite-order invariants

Provides a classification framework for circle maps

Enhances understanding of homotopy set structure

Abstract

We describe the relation of $r$-similarity and finite-order invariants on the homotopy set $[S^1,Y]=\pi_1(Y)$.