no. 2
Parametrized h-cobordism theory
Annales de l'Institut Fourier, Tome 23 (1973) no. 2, pp. 61-74.

Cet article est un exposé du travail de l’auteur sur la “seconde” obstruction à la déformation d’une pseudo-isotopie sur une variété différentiable compacte en une isotopie. Avec des résultats antérieurs sur la “première” obstruction dus indépendamment à J.B. Wagnoner et l’auteur, la généralisation du théorème de la pseudo-isotopie de J. Cerf au cas non simplement connexe est achevée.

This paper gives an expository account of the author’s work on the “second” obstruction to deforming a pseudo-isotopy on a smooth compact manifold to an isotopy. Using earlier results on the “first” obstruction, due independently to J.B. Wagoner and the author, this completes the generalization of J. Cerf’s pseudo-isotopy theorem to the non-simply-connected case.

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     title = {Parametrized $h$-cobordism theory},
     journal = {Annales de l'Institut Fourier},
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     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {23},
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     year = {1973},
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Hatcher, Allen E. Parametrized $h$-cobordism theory. Annales de l'Institut Fourier, Tome 23 (1973) no. 2, pp. 61-74. doi : 10.5802/aif.456. https://aif.centre-mersenne.org/articles/10.5802/aif.456/

[1] P. Antonelli, D. Burghelea and P. J. Kahn, Gromoll groups, Diff Sn and bilinear constructions of exotic spheres, Bull. A.M.S., 76 (1970), p. 772-777. | Zbl

[2] P. Antonelli, D. Burghelea and P.J. Kahn, The concordance-homotopy groups of geometric automorphism groups. Springer Lecture Notes # 215. | MR | Zbl

[3] J. Cerf, La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie. Publ. Math. I.H.E.S., 39 (1970). | Numdam | MR | Zbl

[4] A. Chenciner, Sur la géométrie des strates de petites codimensions. Thèse, Orsay, 1971.

[5] A. Chenciner and F. Laudenbach, Contribution à une théorie de Smale à un paramètre dans le cas non simplement connexe. Annales Sc. Ec. Norm. Sup., 4e série, t. 3 (1970), p. 409-478. | Numdam | MR | Zbl

[6] A. Hatcher, A K2 obstruction for pseudo-isotopies. Thesis, Stanford University, 1971.

[7] A. Hatcher, The second obstruction for pseudo-isotopes. To appear.

[8] A. Hatcher and F. Quinn, Bordism invariants of intersections of submanifolds. To appear. | Zbl

[9] A. Hatcher and J. B. Wagoner, Pseudo-isotopies of non-simply-connected manifolds and the functor K2. To appear.

[10] J. Milnor, Introduction to algebraic K-theory. Annals of Mathematics Study # 72, Princeton University Press, 1971. | MR | Zbl

[11] J. Milnor, unpublished.

[12] F. Quinn, Thesis, Princeton University, 1969.

[13] R. Thom, Topological models in biology. Topology, 8, p. 313-335. | MR | Zbl

[14] J. B. Wagoner, Algebraic invariants for pseudo-isotopies, Proceedings of Liverpool Singularities Symposium II, Springer-Verlag Lecture. Notes # 209. | MR | Zbl

[15] J. B. Wagoner, On K2 of the Laurent polynomial ring. Amer. J. Math., 93, (1971). | MR | Zbl

[16] C. T. C. Wall, Surgery on compact manifolds. Academic Press, 1970. | MR | Zbl

[17] A. Chenciner, Pseudo-isotopies différentiables et pseudo-isotopies linéaires par morceaux. C.R. Acad. Sc., Paris, t. 270 (1970), 1312-1315. | MR | Zbl

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