American Mathematical Society

Book Review

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MathSciNet review: 1567982
Full text of review: PDF This review is available free of charge.
Book Information:

Author: T. Petrie and J. Randall
Title: Connections, definite forms and four-manifolds
Additional book information: Clarendon Press, Oxford, 1990, 130 pp.\ , US$45.00. ISBN 0-19-853599-6.

S. K. Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983), no. 2, 279–315. MR 710056

S. K. Donaldson, Irrationality and the $h$-cobordism conjecture, J. Differential Geom. 26 (1987), no. 1, 141–168. MR 892034

S. K. Donaldson, Polynomial invariants for smooth four-manifolds, Topology 29 (1990), no. 3, 257–315. MR 1066174, DOI 10.1016/0040-9383(90)90001-Z

S. K. Donaldson and P. B. Kronheimer, The geometry of four-manifolds, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1990. Oxford Science Publications. MR 1079726

Ronald Fintushel and Ronald J. Stern, $\textrm {SO}(3)$-connections and the topology of $4$-manifolds, J. Differential Geom. 20 (1984), no. 2, 523–539. MR 788294

Ronald Fintushel and Ronald J. Stern, Pseudofree orbifolds, Ann. of Math. (2) 122 (1985), no. 2, 335–364. MR 808222, DOI 10.2307/1971306

Daniel S. Freed and Karen K. Uhlenbeck, Instantons and four-manifolds, Mathematical Sciences Research Institute Publications, vol. 1, Springer-Verlag, New York, 1984. MR 757358, DOI 10.1007/978-1-4684-0258-2

Michael Hartley Freedman, The topology of four-dimensional manifolds, J. Differential Geometry 17 (1982), no. 3, 357–453. MR 679066

Michael H. Freedman and Frank Quinn, Topology of 4-manifolds, Princeton Mathematical Series, vol. 39, Princeton University Press, Princeton, NJ, 1990. MR 1201584

Robert Friedman and John W. Morgan, On the diffeomorphism types of certain algebraic surfaces. I, J. Differential Geom. 27 (1988), no. 2, 297–369. MR 925124

[FM2]

-, Smooth 4-manifolds and complex surfaces, Ergeb. Math. Grenzgeb. (3), Springer-Verlag, Berlin, Heidelberg, and New York (to appear).

Mikio Furuta, Homology cobordism group of homology $3$-spheres, Invent. Math. 100 (1990), no. 2, 339–355. MR 1047138, DOI 10.1007/BF01231190

Robert E. Gompf, An infinite set of exotic $\textbf {R}^4$’s, J. Differential Geom. 21 (1985), no. 2, 283–300. MR 816673

[GM]

R. Gompf and T. Mrowka, Irreducible four manifolds need not be complex (to appear).

Robion C. Kirby and Laurence C. Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, Annals of Mathematics Studies, No. 88, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1977. With notes by John Milnor and Michael Atiyah. MR 0645390

H. Blaine Lawson Jr., The theory of gauge fields in four dimensions, CBMS Regional Conference Series in Mathematics, vol. 58, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1985. MR 799712, DOI 10.1090/cbms/058

John Milnor, Lectures on the $h$-cobordism theorem, Princeton University Press, Princeton, N.J., 1965. Notes by L. Siebenmann and J. Sondow. MR 0190942

Clifford Henry Taubes, Self-dual Yang-Mills connections on non-self-dual $4$-manifolds, J. Differential Geometry 17 (1982), no. 1, 139–170. MR 658473

Clifford Henry Taubes, Gauge theory on asymptotically periodic $4$-manifolds, J. Differential Geom. 25 (1987), no. 3, 363–430. MR 882829

C. T. C. Wall, Surgery on compact manifolds, London Mathematical Society Monographs, No. 1, Academic Press, London-New York, 1970. MR 0431216

Review Information:

Reviewer: Robert E. Gompf

Journal: Bull. Amer. Math. Soc. 27 (1992), 179-183
DOI: https://doi.org/10.1090/S0273-0979-1992-00291-4