The conjecture H: A lower bound of cohomologic dimension for an elliptic space

TL;DR

This paper improves conditions for estimating the cohomological dimension of elliptic spaces, providing algebraic and geometric perspectives on Betti numbers and rational homotopy groups.

Contribution

It introduces refined bounds for the cohomological dimension of elliptic spaces, extending previous results with new algebraic and geometric insights.

Findings

Enhanced bounds for Betti numbers and homotopy dimensions

Dual algebraic and geometric approaches to elliptic spaces

Generalization of previous sufficiency conditions

Abstract

The goal of this paper is to ameliorate the sufficients conditions, already established by the first author so that the sum of the numbers of Betti, of 1-connected rational finite CW-complex, is higher than the dimension of his $\mathbb Q$-vectorial space of homotopy, we will present it in two aspects, one algebraic and another geometrical.