# Rational homotopy theory

@inproceedings{Hess2011RationalHT, title={Rational homotopy theory}, author={Kathryn Hess}, year={2011} }

1 The Sullivan model 1.1 Rational homotopy theory of spaces We will restrict our attention to simply-connected spaces. Much of this goes through with nilpotent spaces, but this will keep things easier and less technical. Definition 1. A 1-connected space X is said to be rational if either of the following equivalent conditions holds: 1. π∗X forms a graded Q-vector space. 2. H̃∗X forms a graded Q-vector space. (If no mention of coefficients is made, we are using integral coefficients.) Remark 1…

## 801 Citations

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Rational homotopy theory classically studies the torsion free phenomena in the homotopy category of topological spaces and
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- MathematicsMathematische Zeitschrift
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This paper is a generalization of Moriya (in J Pure Appl Algebra 214(4): 422–439, 2010). We develop the de Rham homotopy theory of not necessarily nilpotent spaces. We use two algebraic objects:…

### The de Rham homotopy theory and differential graded category

- Mathematics
- 2012

This paper is a generalization of Moriya (in J Pure Appl Algebra 214(4): 422–439, 2010). We develop the de Rham homotopy theory of not necessarily nilpotent spaces. We use two algebraic objects:…

### The K-theory cochains of H-spaces and height 1 chromatic homotopy theory

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- 2022

Fix an odd prime p . Let X be a pointed space whose p -completed K-theory KU ∗ p ( X ) is an exterior algebra on a ﬁnite number of odd generators; examples include odd spheres and many H-spaces. We…

### Regularity in the growth of the loop space homology of a finite CW complex

- Mathematics
- 2013

To any path connected topological space X, such that rkHi(X) < ∞ for all i ≥ 0, are associated the following two sequences of integers: bi = rkHi(ΩX) and ri = rkπi+1(X). If X is simply connected, the…

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- Mathematics
- 2010

This work focuses on a generalization of the models for rational homotopy theory developed by D. Sullivan and D. Quillen and p-adic homotopy developed by M. Mandell to K(1)-local homotopy theory. The…

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### Geometric and algebraic aspects of 1-formality

- Mathematics
- 2009

Formality is a topological property, defined in terms of Sullivan's model for a space. In the simply-connected setting, a space is formal if its rational homotopy type is determined by the rational…

### Algebraic models for classifying spaces of fibrations

- Mathematics
- 2022

We prove new structural results for the rational homotopy type of the classifying space B aut(X) of fibrations with fiber a simply connected finite CW-complex X. We first study nilpotent covers of B…

### THE CLASSIFYING SPACE FOR FIBRATIONS AND RATIONAL HOMOTOPY THEORY

- Mathematics
- 2016

Over 50 years ago, Jim Stasheff [33] solved the classification problem for fibrations with fibre a finite CW complex X. He constructed a universal X-fibration of the form: X → UE → Baut(X) with base…

## References

SHOWING 1-2 OF 2 REFERENCES

### Hess: A brief intro (arXiv)

- Hess: A brief intro (arXiv)

### Griffiths and Morgan (geometric perspective) 4. Bousfield and Gugenheim (model categorical perspective)

- Griffiths and Morgan (geometric perspective) 4. Bousfield and Gugenheim (model categorical perspective)