Verifying the Hilali conjecture up to formal dimension twenty

TL;DR

This paper proves the Hilali conjecture for simply connected rationally elliptic spaces with formal dimension up to 20, confirming the conjecture in this specific range.

Contribution

It establishes the validity of the Hilali conjecture for formal dimensions up to twenty, extending the known cases.

Findings

Hilali conjecture verified for formal dimension ≤ 20

Total rational homology dimension bounds rational homotopy dimension in these spaces

Supports the conjecture's validity in low-dimensional cases

Abstract

We prove that in formal dimension $\leq 20$ the Hilali conjecture holds, i.e. that the total dimension of the rational homology bounds from above the total dimension of the rational homotopy for a simply connected rationally elliptic space.