# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1705.04180