Book Review

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MathSciNet review: 1567982

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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.

*An application of gauge theory to four-dimensional topology*, J. Differential Geom.

**18**(1983), no. 2, 279–315. MR

**710056**

*Irrationality and the $h$-cobordism conjecture*, J. Differential Geom.

**26**(1987), no. 1, 141–168. MR

**892034**

*Polynomial invariants for smooth four-manifolds*, Topology

**29**(1990), no. 3, 257–315. MR

**1066174**, DOI 10.1016/0040-9383(90)90001-Z

*The geometry of four-manifolds*, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1990. Oxford Science Publications. MR

**1079726**

*$\textrm {SO}(3)$-connections and the topology of $4$-manifolds*, J. Differential Geom.

**20**(1984), no. 2, 523–539. MR

**788294**

*Pseudofree orbifolds*, Ann. of Math. (2)

**122**(1985), no. 2, 335–364. MR

**808222**, DOI 10.2307/1971306

*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

*The topology of four-dimensional manifolds*, J. Differential Geometry

**17**(1982), no. 3, 357–453. MR

**679066**

*Topology of 4-manifolds*, Princeton Mathematical Series, vol. 39, Princeton University Press, Princeton, NJ, 1990. MR

**1201584**

*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).

*Homology cobordism group of homology $3$-spheres*, Invent. Math.

**100**(1990), no. 2, 339–355. MR

**1047138**, DOI 10.1007/BF01231190

*An infinite set of exotic $\textbf {R}^4$’s*, J. Differential Geom.

**21**(1985), no. 2, 283–300. MR

**816673**

**[GM]**

*Irreducible four manifolds need not be complex*(to appear).

*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**

*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

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

**0190942**

*Self-dual Yang-Mills connections on non-self-dual $4$-manifolds*, J. Differential Geometry

**17**(1982), no. 1, 139–170. MR

**658473**

*Gauge theory on asymptotically periodic $4$-manifolds*, J. Differential Geom.

**25**(1987), no. 3, 363–430. MR

**882829**

*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