july 11 < 21, 2016 rabat, morocco · july 11 < 21, 2016. rabat, morocco . cimpa summer school...

Urtzi Buijs

(joint work with Yves Félix, Aniceto Murillo and Daniel

Tanré)

CIMPA summer school on

Rational Homotopy Theory and its Interactions

Rational homotopy of non-connected

spaces

July 11 < 21, 2016. Rabat, Morocco

CIMPA summer school on

Rational Homotopy Theory and its Interactions

1. A brief introduction

Category of commutative differential Z-graded algebras over Q

Category of simplicial sets

1. A brief introduction

CIMPA summer school on

Rational Homotopy Theory and its Interactions

Theorem

1. A brief introduction

CIMPA summer school on

Rational Homotopy Theory and its Interactions

Theorem

1. A brief introduction

CIMPA summer school on

Rational Homotopy Theory and its Interactions

Theorem

2. The cochain functor

CIMPA summer school on

Rational Homotopy Theory and its Interactions

2. The cochain functor

CIMPA summer school on

Rational Homotopy Theory and its Interactions

2. The cochain functor

CIMPA summer school on

Rational Homotopy Theory and its Interactions

2. The cochain functor

CIMPA summer school on

Rational Homotopy Theory and its Interactions

2. The cochain functor

CIMPA summer school on

Rational Homotopy Theory and its Interactions

2. The cochain functor

CIMPA summer school on

Rational Homotopy Theory and its Interactions

2. The cochain functor

CIMPA summer school on

Rational Homotopy Theory and its Interactions

2. The cochain functor

CIMPA summer school on

Rational Homotopy Theory and its Interactions

2. The cochain functor

CIMPA summer school on

Rational Homotopy Theory and its Interactions

2. The cochain functor

CIMPA summer school on

Rational Homotopy Theory and its Interactions

2. The cochain functor

CIMPA summer school on

Rational Homotopy Theory and its Interactions

3. Points, augmentations and

Maurer-Cartan elements

CIMPA summer school on

Rational Homotopy Theory and its Interactions

3. Points, augmentations and

Maurer-Cartan elements

CIMPA summer school on

Rational Homotopy Theory and its Interactions

3. Points, augmentations and

Maurer-Cartan elements

CIMPA summer school on

Rational Homotopy Theory and its Interactions

3. Points, augmentations and

Maurer-Cartan elements

CIMPA summer school on

Rational Homotopy Theory and its Interactions

3. Points, augmentations and

Maurer-Cartan elements

CIMPA summer school on

Rational Homotopy Theory and its Interactions

3. Points, augmentations and

Maurer-Cartan elements

CIMPA summer school on

Rational Homotopy Theory and its Interactions

3. Points, augmentations and

Maurer-Cartan elements

CIMPA summer school on

Rational Homotopy Theory and its Interactions

CIMPA summer school on

Rational Homotopy Theory and its Interactions

3. Points, augmentations and

Maurer-Cartan elements

CIMPA summer school on

Rational Homotopy Theory and its Interactions

3. Points, augmentations and

Maurer-Cartan elements

CIMPA summer school on

Rational Homotopy Theory and its Interactions

3. Points, augmentations and

Maurer-Cartan elements

CIMPA summer school on

Rational Homotopy Theory and its Interactions

3. Points, augmentations and

Maurer-Cartan elements

CIMPA summer school on

Rational Homotopy Theory and its Interactions

3. Points, augmentations and

Maurer-Cartan elements

4. Algebraic models of

non-connected spaces

CIMPA summer school on

Rational Homotopy Theory and its Interactions

CIMPA summer school on

Rational Homotopy Theory and its Interactions

4. Algebraic models of

non-connected spaces

Lemma

Lemma

CIMPA summer school on

Rational Homotopy Theory and its Interactions

4. Algebraic models of

non-connected spaces

Lemma

Theorem

CIMPA summer school on

Rational Homotopy Theory and its Interactions

4. Algebraic models of

non-connected spaces

Corollary

Examples

Examples

CIMPA summer school on

Rational Homotopy Theory and its Interactions

4. Algebraic models of

non-connected spaces

CIMPA summer school on

Rational Homotopy Theory and its Interactions

4. Algebraic models of

non-connected spaces