Parametrized h -cobordism theory

Allen E. Hatcher

Annales de l'institut Fourier (1973)

  • Volume: 23, Issue: 2, page 61-74
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Hatcher, Allen E.. "Parametrized $h$-cobordism theory." Annales de l'institut Fourier 23.2 (1973): 61-74. <http://eudml.org/doc/74130>.

@article{Hatcher1973,
abstract = {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.},
author = {Hatcher, Allen E.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {61-74},
publisher = {Association des Annales de l'Institut Fourier},
title = {Parametrized $h$-cobordism theory},
url = {http://eudml.org/doc/74130},
volume = {23},
year = {1973},
}

TY - JOUR
AU - Hatcher, Allen E.
TI - Parametrized $h$-cobordism theory
JO - Annales de l'institut Fourier
PY - 1973
PB - Association des Annales de l'Institut Fourier
VL - 23
IS - 2
SP - 61
EP - 74
AB - 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.
LA - eng
UR - http://eudml.org/doc/74130
ER -

References

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  1. [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. Zbl0195.53303
  2. [2] P. ANTONELLI, D. BURGHELEA and P.J. KAHN, The concordance-homotopy groups of geometric automorphism groups. Springer Lecture Notes # 215. Zbl0222.57001MR50 #11293
  3. [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). Zbl0213.25202MR45 #1176
  4. [4] A. CHENCINER, Sur la géométrie des strates de petites codimensions. Thèse, Orsay, 1971. 
  5. [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. Zbl0236.57015MR44 #3328
  6. [6] A. HATCHER, A K2 obstruction for pseudo-isotopies. Thesis, Stanford University, 1971. 
  7. [7] A. HATCHER, The second obstruction for pseudo-isotopes. To appear. Zbl0255.57014
  8. [8] A. HATCHER and F. QUINN, Bordism invariants of intersections of submanifolds. To appear. Zbl0291.57019
  9. [9] A. HATCHER and J. B. WAGONER, Pseudo-isotopies of non-simply-connected manifolds and the functor K2. To appear. 
  10. [10] J. MILNOR, Introduction to algebraic K-theory. Annals of Mathematics Study # 72, Princeton University Press, 1971. Zbl0237.18005MR50 #2304
  11. [11] J. MILNOR, unpublished. 
  12. [12] F. QUINN, Thesis, Princeton University, 1969. 
  13. [13] R. THOM, Topological models in biology. Topology, 8, p. 313-335. Zbl0165.23301MR39 #6629
  14. [14] J. B. WAGONER, Algebraic invariants for pseudo-isotopies, Proceedings of Liverpool Singularities Symposium II, Springer-Verlag Lecture. Notes # 209. Zbl0214.22403MR50 #1266
  15. [15] J. B. WAGONER, On K2 of the Laurent polynomial ring. Amer. J. Math., 93, (1971). Zbl0217.34802MR43 #2053
  16. [16] C. T. C. WALL, Surgery on compact manifolds. Academic Press, 1970. Zbl0219.57024MR55 #4217
  17. [17] A. CHENCINER, Pseudo-isotopies différentiables et pseudo-isotopies linéaires par morceaux. C.R. Acad. Sc., Paris, t. 270 (1970), 1312-1315. Zbl0195.25301MR42 #2489

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