On [L]-homotopy groups

TL;DR

This paper investigates properties of [L]-homotopy groups for finite complexes L, demonstrating that for certain L, the n-th [L]-homotopy group of Sn is isomorphic to Z, extending understanding of homotopy group structures.

Contribution

It establishes that for complexes L with extension type between Sn and Sn+1, the n-th [L]-homotopy group of Sn is isomorphic to Z, providing new insights into [L]-homotopy theory.

Findings

For complex L with extension type between Sn and Sn+1, the n-th [L]-homotopy group of Sn is Z.

Properties of [L]-homotopy groups for finite complexes L are characterized.

Extension type influences the structure of [L]-homotopy groups.

Abstract

Some properties of [L]-homotopy group for finite complex L are investigated. It is proved that for complex L whose extension type lying between Sn and Sn+1 n-th [L]-homotopy group of Sn is isomorphic to Z.