Rational homotopy -- Sullivan models

TL;DR

This paper introduces Sullivan models in rational homotopy theory, demonstrating their use in computing free loop space models and proving a key theorem on Betti numbers.

Contribution

It provides the first explicit Sullivan model for free loop spaces and applies it to prove the Vigué-Poirrier-Sullivan theorem.

Findings

Sullivan models of free loop spaces are constructed.

The Vigué-Poirrier-Sullivan theorem is proved using these models.

The approach advances understanding of rational homotopy invariants.

Abstract

This chapter is a short introduction to Sullivan models. In particular, we find the Sullivan model of a free loop space and use it to prove the Vigu\'e-Poirrier-Sullivan theorem on the Betti numbers of a free loop space.