Pseudo-isotopies of irreducible 3-manifolds

Kiralis, Jeff

doi:10.1090/S0002-9947-1992-1140917-6

Pseudo-isotopies of irreducible $3$-manifolds
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by Jeff Kiralis

Trans. Amer. Math. Soc. 332 (1992), 53-78

DOI: https://doi.org/10.1090/S0002-9947-1992-1140917-6

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Abstract:

It is shown that a certain subspace of the space of all pseudo-isotopies of any irreducible $3$-manifold is connected. This subspace consists of those pseudo-isotopies corresponding to $1$-parameter families of functions which have nondegenerate critical points of index $1$ and $2$ only and which contain no slides among the $2$-handles. Some of the techniques developed are used to prove a weak four-dimensional $h$-cobordism theorem.

References

Jean Cerf, La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie, Inst. Hautes Études Sci. Publ. Math. 39 (1970), 5–173 (French). MR 292089
David Gabai, Foliations and the topology of $3$-manifolds, J. Differential Geom. 18 (1983), no. 3, 445–503. MR 723813
A. Hatcher, On the diffeomorphism group of $S^{1}\times S^{2}$, Proc. Amer. Math. Soc. 83 (1981), no. 2, 427–430. MR 624946, DOI 10.1090/S0002-9939-1981-0624946-2
Allen E. Hatcher, A proof of the Smale conjecture, $\textrm {Diff}(S^{3})\simeq \textrm {O}(4)$, Ann. of Math. (2) 117 (1983), no. 3, 553–607. MR 701256, DOI 10.2307/2007035
Allen Hatcher and John Wagoner, Pseudo-isotopies of compact manifolds, Astérisque, No. 6, Société Mathématique de France, Paris, 1973. With English and French prefaces. MR 0353337
Harrie Hendriks and François Laudenbach, Difféomorphismes des sommes connexes en dimension trois, Topology 23 (1984), no. 4, 423–443. MR 780734, DOI 10.1016/0040-9383(84)90004-1
François Laudenbach and Valentin Poénaru, A note on $4$-dimensional handlebodies, Bull. Soc. Math. France 100 (1972), 337–344. MR 317343

Lectures on the

cobordism theorem

Morse theory