These are the proceedings of the Summer Research Conference on 4-manifolds held at Durham, New Hampshire, July 1982, under the auspices of the American Mathematical Society and National Science Foundation. The conference was highlighted by the breakthroughs of Michael Freedman and S. K. Donaldson and by Frank Quinn's completion at the conference of the proof of the annulus conjecture. (We commend the AMS committee, particularly Julius Shaneson, who had the foresight in Spring 1981 to choose the subject, 4-manifolds, in which such remarkable activity was imminent.) Freedman and several others spoke on his work; some of their talks are represented by papers in this volume.Donaldson and Clifford H. Taubes gave surveys of their work on gauge theory and 4-manifolds and their papers are also included herein. There were a variety of other lectures, including Quinn's surprise, and a couple of problem sessions which led to the problem list. A background of basic differential topology is adequate for potential readers.
Fibered knots and involutions on homotopy spheres by I. R. Aitchison and J. H. Rubinstein A fake $4$-manifold by S. Akbulut Approximating cell-like maps of $S^4$ by homeomorphisms by F. D. Ancel Linking numbers in branched covers by S. E. Cappell and J. L. Shaneson Atomic surgery problems by A. Casson and M. Freedman Smooth $4$-manifolds with definite intersection form by S. K. Donaldson The solution of the $4$-dimensional annulus conjecture (after Frank Quinn) by R. D. Edwards A $\mu$-invariant one homology $3$-sphere that bounds an orientable rational ball by R. Fintushel and R. J. Stern Another construction of an exotic $S^1\times S^3\,\ No. \,S^2\times S$2$ by R. Fintushel and R. J. Stern On Freedman's reimbedding theorems by R. E. Gompf and S. Singh The homology of the mapping class group and its connection to surface bundles over surfaces by J. Harer Rochlin invariant and $\alpha$-invariant by A. Kawuchi Cobordism of satellite knots by R. A. Litherland Complex structures on $4$-manifolds by R. Mandelbaum Good torus fibrations by Y. Matsumoto $4$-dimensional oriented bordism by P. Melvin A new proof of the homology torus and annulus theorem by R. T. Miller Fibered knots in $S^4$-twisting, spinning, rolling, surgery, and branching by S. P. Plotnick The embedding theorem for towers by F. Quinn Smooth structures on $4$-manifolds by F. Quinn Concordance of links in $S^4$ by D. Ruberman Constructions of quasipositive knots and links, II by L. Rudolph An introduction to self-dual connections by C. H. Taubes $4$-manifold problems by R. Kirby.