Contemporary Mathematics 1985; 528 pp; softcover Volume: 35 Reprint/Revision History: reprinted 1988 ISBN10: 0821850334 ISBN13: 9780821850336 List Price: US$72 Member Price: US$57.60 Order Code: CONM/35
 These are the proceedings of the Summer Research Conference on 4manifolds 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, 4manifolds, 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 4manifolds 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. Table of Contents  I. R. Aitchison and J. H. Rubinstein  Fibered knots and involutions on homotopy spheres
 S. Akbulut  A fake \(4\)manifold
 F. D. Ancel  Approximating celllike maps of \(S^4\) by homeomorphisms
 S. E. Cappell and J. L. Shaneson  Linking numbers in branched covers
 A. Casson and M. Freedman  Atomic surgery problems
 S. K. Donaldson  Smooth \(4\)manifolds with definite intersection form
 R. D. Edwards  The solution of the \(4\)dimensional annulus conjecture (after Frank Quinn)
 R. Fintushel and R. J. Stern  A \(\mu\)invariant one homology \(3\)sphere that bounds an orientable rational ball
 R. Fintushel and R. J. Stern  Another construction of an exotic \(S^1\times S^3\,\#\,S^2\times S^2\)
 R. E. Gompf and S. Singh  On Freedman's reimbedding theorems
 J. Harer  The homology of the mapping class group and its connection to surface bundles over surfaces
 A. Kawuchi  Rochlin invariant and \(\alpha\)invariant
 R. A. Litherland  Cobordism of satellite knots
 R. Mandelbaum  Complex structures on \(4\)manifolds
 Y. Matsumoto  Good torus fibrations
 P. Melvin  \(4\)dimensional oriented bordism
 R. T. Miller  A new proof of the homology torus and annulus theorem
 S. P. Plotnick  Fibered knots in \(S^4\)twisting, spinning, rolling, surgery, and branching
 F. Quinn  The embedding theorem for towers
 F. Quinn  Smooth structures on \(4\)manifolds
 D. Ruberman  Concordance of links in \(S^4\)
 L. Rudolph  Constructions of quasipositive knots and links, II
 C. H. Taubes  An introduction to selfdual connections
 R. Kirby  \(4\)manifold problems
