Geometric approach towards stable homotopy groups of spheres. Kervaire Invariant

TL;DR

This paper proves that for dimensions up to a certain bound, framed manifolds have a trivial Kervaire invariant, advancing understanding of stable homotopy groups of spheres.

Contribution

It establishes the existence of an integer L such that all framed manifolds of dimension 2^l - 2, with l ≤ L, have trivial Kervaire invariant, providing a key result in topology.

Findings

Existence of an integer L for trivial Kervaire invariant in certain dimensions

Framed manifolds of dimension 2^l - 2 have trivial Kervaire invariant for l ≤ L

Advances understanding of stable homotopy groups of spheres

Abstract

It is proved that there exists an integer $L$ such that a framed manifold of dimension $2^l-2$, $l\le L$ has the trivial Kervaire Invariant.