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A survey of the foundations of four-manifold theory in the topological category
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This survey aims to provide a guide to the literature on topological 4-manifolds. Foundational theorems on 4-manifolds are stated, especially in the topological category. Precise references are given, with indications of the strategies employed in the proofs. Where appropriate we give statements for manifolds of all dimensions. Many intuitively plausible theorems which are standard results in differential topology are either extraordinarily deep results in the topological category, are open, or are known to be false. Hence one must proceed with caution. This book seeks to help 4-manifold topologists navigate potential pitfalls, and to apply the many powerful results that do exist with confidence.
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Cited by 2 Pith papers
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Regularity of Resolutions and Limits of Manifolds with a Uniform Contractibility Function
If a compact ANR is a Gromov-Hausdorff limit of closed n-manifolds with bounded contractibility functions, then it is an open cell-like image of each sufficiently close approximating manifold, resolving Moore's conjec...
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Simply slicing knots
A knot K bounds a locally flat Z_d-disc representing a class x of divisibility d in a simply-connected 4-manifold N iff its Arf invariant matches a congruence and b_2(N) dominates all Levine-Tristram signature bounds.
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