TABLE OF CONTENTS Notations vii Introduction 1 Section 1. Distributions 7 1.1. Definitions 7 1.2. Kernel theorems 7 1.3. Decomposition lemma 8 Section 2. Differential homological algebra 10 2.1. Definitions 10 2.2. Twisted tensor products 14 2.3. Minimal extensions of differential graded algebras 15 2.4. Differential graded modules with group actions 18 2.5. Koszul differential graded modules ..... 19 2.6. Kunneth theorems 20 2.7. Differential torsion products 21 2.8. Simplicial de Rham functor 25 2.9. Differential graded modules over a manifold 26 Section 3. Lie algebra cohomology 28 3.1. Definitions 28 3.2. Differential graded modules with Lie algebra actions 31 3.3. Cohomology of L„ 32 3.4. Weil algebras 34 Section 4. Frame bundles of manifolds 37 4.1. Group of formal diffeomorphisms 37 4.2. Frame bundles 38 Section 5. Statements of the main results 41 5.1. The fundamental theorem 41 5.2. Topological interpretation of H(LM, FM) ..... 44 5.3. Compact support coefficients 47 5.4. Distribution coefficients 47 5.5. The case of L^ 50 M iii
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