Models in Rational homotopy theory and Torus Rank Conjecture

TL;DR

This paper explores various models in rational homotopy theory, establishes connections among them, and applies these insights to prove the long-standing Torus Rank Conjecture.

Contribution

It introduces connections between different rational homotopy models and uses these to prove the Torus Rank Conjecture for the first time.

Findings

Established links between Sullivan, Quillen, C_infinity, and L_infinity models.

Proved the Torus Rank Conjecture using these models.

Enhanced understanding of rational homotopy models and their applications.

Abstract

In this paper, we focus on some models in rational homotopy theory, Sullivan model, Quillen model, C_\infty model, and L_\infty model. We give some connections between them. As an application, we prove the Torus Rank Conjecture.