Differential Topology by A. Banyaga (auth.), Prof. Vinicio Villani (eds.)

By A. Banyaga (auth.), Prof. Vinicio Villani (eds.)

A. Banyaga: at the team of diffeomorphisms keeping a precise symplectic.- G.A. Fredricks: a few feedback on Cauchy-Riemann structures.- A. Haefliger: Differentiable Cohomology.- J.N. Mather: at the homology of Haefliger’s classifying space.- P. Michor: Manifolds of differentiable maps.- V. Poenaru: a few feedback on low-dimensional topology and immersion theory.- F. Sergeraert: los angeles classe de cobordisme des feuilletages de Reeb de S³ est nulle.- G. pockets: Invariant de Godbillon-Vey et difféomorphismes commutants.

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Paris 270 A 640-2. 191 C. Chevalley-S. Eilenberg. Cohomology theory of Lie groups and Lie algebras - Trans. AMS, 63 (1948) 85-124. [lo] 'Dupont - Simplicia1 de Rham cohomology and characteristic classes of flat bundles, Topology 15 (1976) 233-245. [ 11 1 C. Ehresmam. Les connexions in£initgsimales dans un fibr6 dif f6rentiable Colloque de Topologie de Bruxelles 1950. CBRM, 29-55. 112; Van Est - On the algebraic cohomology concepts in Lie groups. Nedel Akad. Wetensch. Proc. Ser. A 58 (1955) I, 225-233 ; 11, 286-294.

The groupoid rM (cf. I,7). III,i) can be considered as a differentiable groupoid, 'l M being a differentiable n-manifold, but not Hausdorff. On rM, one can consider another topology ; roughly two germs are closed together if their jets are close. For a precise definition, k let J rM be the differentiable groupoid of k-jets of local diffeomorphisms of M ; it is a differentiable manifold (compare with I,8) ; with the source We define JrM projection, it is a bundle with fiber isomorphic to pk M' k as the inverse limit of the J r ;it will be considered as some kind of M differentiable groupoid.

AMS 77 (1971) 1111-1115. 1381 J. Mather. ~ntegrability in codimension I, Co~mn,Math, Helv. 48 (1973) 195-233. C391 J. Mather. Commutators of diffeomorphisms I and 11, Conrm. Mith. Helv. 49, (1974), p. MOS~OW. Cohomology of Topological groups and ~olvmanifolds. Ann. of Math. (1961), 20-48. 1411 P. Molino. Classes caractIristiques et obstructions dlAtiyah pour les fibres principaux feuilletgs. R, Acad. Sc. Paris 272 (1971). [421 C. Roger. MIthodes homotopiques et cohomologiques en thIorie des feuilletages.

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