Differential Topology: Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Varenna (Como), Italy, ... 4, 1976 (C.I.M.E. Summer Schools, 73)

A. Banyaga: On the group of diffeomorphisms preserving an exact symplectic.- G.A. Fredricks: Some remarks on Cauchy-Riemann structures.- A. Haefliger: Differentiable Cohomology.- J.N. Mather: On the homology of Haefliger’s classifying space.- P. Michor: Manifolds of differentiable maps.- V. Poenaru: Some remarks on low-dimensional topology and immersion theory.- F. Sergeraert: La classe de cobordisme des feuilletages de Reeb de S3 est nulle.- G. Wallet: Invariant de Godbillon-Vey et difféomorphismes commutants. Cover Differential Topology ISBN 9783642111013 Contents On the Group of Diffeomorphisms Preserving an Exact Symplectic Form Statement of the result References Some Remarks on Cauchy-Riemann Structures References Differentiable Cohomology Chapter I: Invariant forms 1. Basic formulas. (cf. [32]) 2. Cartan Theorems 3. Cohomology of Lie algebras (cf. [9] et [33]) 4. K-basic forms and relative cohomology of Lie algebras 5. Bundle with discrete structural group and characteristic homomorphism 6. Main example 7. Invariant forms on groups of deffeomorphisms 8. Invariant forms on frames bundle Chapter II - Differentiable Cohomology of LIE Groups 1. Cohomology of discrete groups (see for instance [1]) 2. Continuous and differentiable cohomoloty of Lie groups 3. Van Est theorem 4. Comparison between cohomology and differentiable cohomology 5. Case of the group of diffeomorphisms Chapter III - Cohomology Theory for Topological Groupoïds* 1. Topological groupoids and homomorphisms. Examples (cf. [24]) 2. Abstract cohomology theory for 3. Standard resolutions (compare with II,1) 4. Construction of cohomology 5. Resolution using differential form 6. Formulation in the framework of relative homological algebra (cf. Mac Lane [36]) Chapter IV: Differentiable Cohomology of Groupoids with Two Differentiable Structures 1. Examples of such groupords 2. Differentiable cohomology of (Image) with real coefficient 3. Typical smooth(Image)-sheaves 4. Differentiable cohomology of (Image) with real coefficient 5. Differentiable cohomology with coefficient in E. 6. Conclusion References On the Homology of Haefliger's Classifying Space 1. Haefliger Structures (Deifinition) 2. The Classifying Space for Cap gamma - structures 3. The Normal Bundle 4. The Classifying Theorem 5. Model for BG. 6. Thurston's theorem 7. Cap gamma - Btructures Transverse to the Fibers 8. Local Model for Image 9. Disk model for Image 10. First Deformation Lama 11. A Homotopy 12. Proof of the First Deformation Lemma 13. Existence of Gn 14. Second Deformation Lemma 15. Proof of the second deformation lemma 16. Spme of Sections 17. Construction of the Mapping 18. Filtrations of XM and Image 19. Construction of Image etc. 20. Construction of Image etc 21 Topology of Image etc 22. Topology of Image 23. Construction of Image 24. Construction of Image 25. End of the Proof of the Lemrma in § 21 26. A Property of the Functor vN 27. Proof of the Corollary of Thurston's Theorem 28. Proof of Thurston's Theorem References Manifolds of differentiable maps References Some remarks on low-dimensional topology and immersion theory References La Classe de Cobordisme des Feuilletages de Reeb de S3 Est Nulle Bibliographie Invariant de Godbillon-Vey et Diffeomorphismes Commutants I. Definition de l'homomorphisme GV et enonce du resultat principal II. Reduction du theoreme 1 à un cas particulier III. Centralisateur de certains diffeomorphisme IV. Demonstration du theoreme 2 dans le cas dg la proposition 1 V. Une presentation simpliciale de l'homomorphision GV VI. Fin de la demonstration du theoreme 2 Biblographie Includes topics suah as: On the group of diffeomorphisms preserving an exact symplectic; Some remarks on Cauchy-Riemann structures; Differentiable Cohomology; On the homology of Haefliger's classifying space; Manifolds of differentiable maps; and, Some remarks on low-dimensional topology and immersion theory. Banyaga: On the group of diffeomorphisms preserving an exact symplectic.- G.A. Poenaru: Some remarks on low-dimensional topology and immersion theory.- F. Sergeraert: La classe de cobordisme des feuilletages de Reeb de S(3) est nulle.- G. Wallet: Invariant de Godbillon-Vey et diffeomorphismes commutants.