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)

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