**Memoirs of the American Mathematical Society**

2000;
149 pp;
Softcover

MSC: Primary 55;
Secondary 57; 17; 20; 18

Print ISBN: 978-0-8218-1920-3

Product Code: MEMO/143/682

List Price: $57.00

AMS Member Price: $34.20

MAA Member Price: $51.30

**Electronic ISBN: 978-1-4704-0273-0
Product Code: MEMO/143/682.E**

List Price: $57.00

AMS Member Price: $34.20

MAA Member Price: $51.30

# Rational Homotopical Models and Uniqueness

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*Martin Majewski*

Abstract. The main goal of this paper is to prove the following conjecture of Baues and Lemaire: the differential graded Lie algebra associated with the Sullivan model of a space is homotopy equivalent to its Quillen model. In addition we show the same for the cellular Lie algebra model which we build from the simplicial analog of the classical Adams - Hilton model. It turns out that this cellular Lie algebra model is one link in a chain of models connecting the models of Quillen and Sullivan. The key result which makes all this possible is Anick's correspondence between differential graded Lie algebras and Hopf algebras up to homotopy. In addition we show that the Quillen model is a rational homotopical equivalence, and we conclude the same for the other models using our main result. The construction of the three models is given in detail. The background from homotopy theory, differential algebra, and algebra is presented in great generality.

#### Readership

Graduate students and research mathematicians interested in algebraic topology.

#### Table of Contents

# Table of Contents

## Rational Homotopical Models and Uniqueness

- TABLE OF CONTENTS vii8 free
- ABSTRACT x11 free
- KEYWORDS x11
- PREFACE xi12 free
- INTRODUCTION xiii14 free
- 1. HOMOTOPY THEORY 120 free
- 2. DIFFERENTIAL ALGEBRA 2544
- 3. COMPLETE ALGEBRA 5776
- 4. THREE MODELS FOR SPACES 97116
- NOTATIONS 145164
- BIBLIOGRAPHY 147166