Rational homotopy theory via Sullivan models: a survey

TL;DR

This survey reviews the development and current state of rational homotopy theory using Sullivan models, highlighting key results, applications, and open problems in the field.

Contribution

It provides a comprehensive overview of rational homotopy theory with Sullivan models, including recent advances and open research questions.

Findings

Summarizes main results in rational homotopy theory.

Highlights applications of rational homotopy in various areas.

Identifies important open problems in the field.

Abstract

This survey contains the main results in rational homotopy, from the beginning to the most recent ones. It makes the status of the art, gives a short presentation of some areas where rational homotopy has been used, and contains a lot of important open problems