The stability theorem for smooth pseudoisotopies
- 1 January 1988
- Vol. 2 (1-2) , 1-355
- https://doi.org/10.1007/bf00533643
Abstract
The stability theorem states that the suspension map C(M) ? C(M X I) defined on the pseudoisotopy space C(M)=Diff(M X I rel M X O U ?M X I) of a compact smooth n-manifold M is ~ n/3-connected. This implies that C(M) has the R~ n/3-homotopy type of the stable pseudoisotopy space P(M) which is related to Waldhausen's algebraic K-theory of spaces by Waldhausen's formula A(X) O8S8(X+) X B2P(X). This paper gives a detailed proof of the smooth stability theorem following ideas by Hatcher for the proof of a PL stability theorem.Keywords
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