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Four-Manifold Theory
Edited by: Cameron Gordon and Robion C. Kirby
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Contemporary Mathematics
1985; 528 pp; softcover
Volume: 35
Reprint/Revision History:
reprinted 1988
ISBN-10: 0-8218-5033-4
ISBN-13: 978-0-8218-5033-6
List Price: US$68
Member Price: US$54.40
Order Code: CONM/35
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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.

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 cell-like 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 self-dual connections
  • R. Kirby -- \(4\)-manifold problems
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