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.
@article{AIF_1973__23_2_61_0,
author = {Hatcher, Allen E.},
title = {Parametrized $h$-cobordism theory},
journal = {Annales de l'Institut Fourier},
pages = {61--74},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {23},
number = {2},
year = {1973},
doi = {10.5802/aif.456},
mrnumber = {50 #1267},
zbl = {0259.57016},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.456/}
}
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. http://www.numdam.org/articles/10.5802/aif.456/
[1] , and , Gromoll groups, Diff Sn and bilinear constructions of exotic spheres, Bull. A.M.S., 76 (1970), p. 772-777. | Zbl
[2] , and , The concordance-homotopy groups of geometric automorphism groups. Springer Lecture Notes # 215. | MR | Zbl
[3] , 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] , Sur la géométrie des strates de petites codimensions. Thèse, Orsay, 1971.
[5] and , 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 K2 obstruction for pseudo-isotopies. Thesis, Stanford University, 1971.
[7] , The second obstruction for pseudo-isotopes. To appear.
[8] and , Bordism invariants of intersections of submanifolds. To appear. | Zbl
[9] and , Pseudo-isotopies of non-simply-connected manifolds and the functor K2. To appear.
[10] , Introduction to algebraic K-theory. Annals of Mathematics Study # 72, Princeton University Press, 1971. | MR | Zbl
[11] , unpublished.
[12] , Thesis, Princeton University, 1969.
[13] , Topological models in biology. Topology, 8, p. 313-335. | MR | Zbl
[14] , Algebraic invariants for pseudo-isotopies, Proceedings of Liverpool Singularities Symposium II, Springer-Verlag Lecture. Notes # 209. | MR | Zbl
[15] , On K2 of the Laurent polynomial ring. Amer. J. Math., 93, (1971). | MR | Zbl
[16] , Surgery on compact manifolds. Academic Press, 1970. | MR | Zbl
[17] , 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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