A generalized Kervaire Problem in stable homotopy groups of spheres

TL;DR

This paper provides an elementary description of the Mahowald element in stable homotopy groups and proves a generalized Kervaire Problem has a positive solution, advancing understanding in algebraic topology.

Contribution

It introduces a new elementary construction of the Mahowald element and solves a generalized Kervaire Problem in stable homotopy groups.

Findings

Elementary self-contained description of the Mahowald element

Positive solution to the generalized Kervaire Problem

Enhanced understanding of stable homotopy groups of spheres

Abstract

We will give an elementary self-contained description of the Mahowald element in the stable homotopy group of spheres $\Pi_{2^l}$, $l \ge 3$. Using this construction, we prove that a generalized Kervaire Problem, formulated by the author in \cite{A} is solved positively.