A survey of the foundations of four-manifold theory in the topological category

Abstract

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.

155 pages, 14 figures. Comments very welcome. Version 2 includes corrections to Theorems 2.7, 8.2, and 11.6. Version 3 has been extensively rewritten following a referee report, including new chapters 3 and 7