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Book DetailsContemporary MathematicsVolume: 35; 1985; 528 ppMSC: Primary 57;
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

Articles

I. R. Aitchison and J. H. Rubinstein  Fibered knots and involutions on homotopy spheres [ MR 780575 ]

Selman Akbulut  A fake $4$manifold [ MR 780576 ]

Fredric D. Ancel  Approximating celllike maps of $S^4$ by homeomorphisms [ MR 780577 ]

Sylvain E. Cappell and Julius L. Shaneson  Linking numbers in branched covers [ MR 780578 ]

Andrew Casson and Michael Freedman  Atomic surgery problems [ MR 780579 ]

S. K. Donaldson  Smooth $4$manifolds with definite intersection form [ MR 780580 ]

Robert D. Edwards  The solution of the $4$dimensional annulus conjecture (after Frank Quinn) [ MR 780581 ]

Ronald Fintushel and Ronald J. Stern  A $\mu $invariant one homology $3$sphere that bounds an orientable rational ball [ MR 780582 ]

Ronald Fintushel and Ronald J. Stern  Another construction of an exotic $S^1 \stackrel {\times }{\sim } S^3\# S^2\times S^2$ [ MR 780583 ]

Robert E. Gompf and Sukhjit Singh  On Freedman reimbedding theorems [ MR 780584 ]

John Harer  The homology of the mapping class group and its connection to surface bundles over surfaces [ MR 780585 ]

Akio Kawauchi  Rochlin invariant and $\alpha $invariant [ MR 780586 ]

R. A. Litherland  Cobordism of satellite knots [ MR 780587 ]

Richard Mandelbaum  Complex structures on $4$manifolds [ MR 780588 ]

Yukio Matsumoto  Good torus fibrations [ MR 780589 ]

Paul Melvin  $4$dimensional oriented bordism [ MR 780590 ]

Richard T. Miller  A new proof of the homotopy torus and annulus theorem [ MR 780591 ]

Steven P. Plotnick  Fibered knots in $S^4$—twisting, spinning, rolling, surgery, and branching [ MR 780592 ]

Frank Quinn  The embedding theorem for towers [ MR 780593 ]

Frank Quinn  Smooth structures on $4$manifolds [ MR 780594 ]

Daniel Ruberman  Concordance of links in $S^4$ [ MR 780595 ]

Lee Rudolph  Constructions of quasipositive knots and links. II [ MR 780596 ]

Clifford Henry Taubes  An introduction to selfdual connections [ MR 780597 ]

Edited by Rob Kirby  $4$manifold problems [ MR 780598 ]


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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.

Articles

I. R. Aitchison and J. H. Rubinstein  Fibered knots and involutions on homotopy spheres [ MR 780575 ]

Selman Akbulut  A fake $4$manifold [ MR 780576 ]

Fredric D. Ancel  Approximating celllike maps of $S^4$ by homeomorphisms [ MR 780577 ]

Sylvain E. Cappell and Julius L. Shaneson  Linking numbers in branched covers [ MR 780578 ]

Andrew Casson and Michael Freedman  Atomic surgery problems [ MR 780579 ]

S. K. Donaldson  Smooth $4$manifolds with definite intersection form [ MR 780580 ]

Robert D. Edwards  The solution of the $4$dimensional annulus conjecture (after Frank Quinn) [ MR 780581 ]

Ronald Fintushel and Ronald J. Stern  A $\mu $invariant one homology $3$sphere that bounds an orientable rational ball [ MR 780582 ]

Ronald Fintushel and Ronald J. Stern  Another construction of an exotic $S^1 \stackrel {\times }{\sim } S^3\# S^2\times S^2$ [ MR 780583 ]

Robert E. Gompf and Sukhjit Singh  On Freedman reimbedding theorems [ MR 780584 ]

John Harer  The homology of the mapping class group and its connection to surface bundles over surfaces [ MR 780585 ]

Akio Kawauchi  Rochlin invariant and $\alpha $invariant [ MR 780586 ]

R. A. Litherland  Cobordism of satellite knots [ MR 780587 ]

Richard Mandelbaum  Complex structures on $4$manifolds [ MR 780588 ]

Yukio Matsumoto  Good torus fibrations [ MR 780589 ]

Paul Melvin  $4$dimensional oriented bordism [ MR 780590 ]

Richard T. Miller  A new proof of the homotopy torus and annulus theorem [ MR 780591 ]

Steven P. Plotnick  Fibered knots in $S^4$—twisting, spinning, rolling, surgery, and branching [ MR 780592 ]

Frank Quinn  The embedding theorem for towers [ MR 780593 ]

Frank Quinn  Smooth structures on $4$manifolds [ MR 780594 ]

Daniel Ruberman  Concordance of links in $S^4$ [ MR 780595 ]

Lee Rudolph  Constructions of quasipositive knots and links. II [ MR 780596 ]

Clifford Henry Taubes  An introduction to selfdual connections [ MR 780597 ]

Edited by Rob Kirby  $4$manifold problems [ MR 780598 ]