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Atomic surgery problems. (English) Zbl 0559.57008

Four-manifold theory, Proc. AMS-IMS-SIAM Joint Summer Res. Conf., Durham/N.H. 1982, Contemp. Math. 35, 181-199 (1984).
[For the entire collection see Zbl 0549.00018.]
The second author’s own review: ”This is a preliminary draft, written and abandoned in 1976 (or 1977). Andrew had come to visit me; I put him to work on the non-simply-connected version of his theory of flexible handle-bodies. This writeup explores the finite version, though we considered, but could find no use for the non-compact limit (recently considered in Dimonski’s Ph. D. thesis). This paper is included in the proceedings at the request of the editors, as an historic relic. Two recent ideas which we suffered in ignorance of were: 1. It is possible (even when \(\pi_ 1\neq 0)\) to concentrate on complexes which serve as substitutes for a disk rather than ones substituting for a wedge of 2- spheres. And the related observation - 2. The more symmetrical group construction can replace the ”1/2-towers” created here. (Bob Edwards was influential in the development of both these ideas - a fact, I am glad to record.) The second deficit greatly complicates our discussion of the s- cobordism theorem. This draft was never proofed by Andrew, has not been updated, and is probably replete with speling erors!”
Reviewer: R.Stern

MSC:

57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
57R65 Surgery and handlebodies
57R80 \(h\)- and \(s\)-cobordism

Citations:

Zbl 0549.00018