Celebratio Mathematica — Freedman

Topology in dImension 4

Works connected to Wu-Chung Hsiang

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article C. L. Curtis, M. H. Freedman, W. C. Hsiang, and R. Stong: “A decomposition theorem for \( h \)-cobordant smooth simply-connected compact 4-manifolds,” Invent. Math. 123 : 2 (1996), pp. 343–348. MR 1374205 Zbl 0843.57020

Let \( M \) and \( N \) be smooth, \( h \)-cobordant compact 1-connected 4-manifolds. There exist decompositions \[ M = M_0 \cup_{\Sigma}M_1 \quad\text{and}\quad N = N_0 \cup_{\Sigma}N_1 \] where \( M_0 \) and \( N_0 \) are smooth compact contractible 4-manifolds with boundary \( \Sigma \), so that \( (M_1,\Sigma) \), and \( (N_1,\Sigma) \) are diffeomorphic. If \( M \) and \( N \) are closed, then we may further arrange that \( M_1 \) and \( N_1 \) are 1-connected. In fact, if \( W \) is an \( h \)-cobordism connecting \( M \) and \( N \), then \( W \) can be written \[ W = W_0 \cup_{\Sigma\times I}W_1 \] where \( (W_0;M_0,N_0) \) is an (often) nontrivial \( h \)-cobordism and \( (W_1;M_1,N_1) \) is smoothly the product \( h \)-cobordism \[ (M_1\times I;\,M_1\times\{0\},\,M_1\times\{1\}) .\]

Wu-Chung Hsiang	Related
Cynthia Louise Curtis	Related
Richard Stong	Related