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

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

A. Banyaga: at the staff of diffeomorphisms protecting an actual symplectic.- G.A. Fredricks: a few comments 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: l. a. classe de cobordisme des feuilletages de Reeb de S³ est nulle.- G. pockets: Invariant de Godbillon-Vey et difféomorphismes commutants.

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Example text

Ca(r M ; %en as in III,S, we get a homomorphism of * in the Cech-de Rham complex C*(Q; R*), hence a characteristic homomorphism X If we compose the isomorphism H*(an ; On) + Ha ( rM ; R) with this characteristic homomorphism, we get the homomorphism described directly in [ 21 [ 61 [251. An example. u = (y )*u). An M element u of cP(rM; $ associates to a composable Gequence yl.. ',y an P $, where - s(y 'lhe differential 6 is element w(yl,. ,y P P = )E x ). We want to show that the formula given by Thurston for the GodbillonVey invariant in the complex C*(r ,R*R) can be proved following the preceding d 1 proof.

Also according to [491, H*(s ) is, in degreej;Zn, a polynomial algebra in a generator of degree 2 ; on the other hand in degree 2n,Bi;n i s a n Eilenberg-MacLane complex K(R ; 2), The Hochshild- Serre spectral sequence relating H*(+ ) and H* Serre spectral sequence of the fibration (S ) BFu BTn ' + correspond to the REFERENCES [ 11 Atiyah-Wall. - Cohomology of groups. Algebraic 'number theory edited by Cassels and Frzlich - Academic Press (1967), 94-115. N. Rosenfeld- On Characteric classes of foliations - Functional Analysis and applications, 6 (1972), 68-69 - [3] A.

Thurston. Existence of codimension one foliations, Ann. of Math. (to appear). 1471 G . Segal. Classifying spaces and spectral sequences. IHES mathktiques No 34 (L - Publications 105-112. 1481 N. Steenrod. The Topology of Fiber Bundles. Princeton University Press 1951. 1491 J . R. Acad. Sc. (1975) 805.

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