Halperin's conjecture in formal dimensions up to 20

TL;DR

This paper extends the proof of Halperin's conjecture for positively elliptic spaces to formal dimensions up to 20, simplifying the proof using algebraic methods.

Contribution

It shortens and extends previous proofs of Halperin's conjecture to higher formal dimensions using elementary algebraic techniques.

Findings

Confirmed Halperin's conjecture up to formal dimension 20

Provided a simplified proof based on polynomial algebras

Extended previous results from dimension 16 to 20

Abstract

A 1976 conjecture of Halperin on positively elliptic spaces was recently confirmed in formal dimensions up to 16. In this article, we shorten the proof and extend the result up to formal dimension 20. We work with Meier's algebraic characterization of the conjecture, so the proof is elementary in that it involves only polynomial algebras, ideals, and derivations.