Book Review

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Book Information:

Authors: Robert Gompf and András Stipsicz

Title: 4-manifolds and Kirby calculus

Additional book information: Amer. Math. Soc., Providence, RI, 1999, xv + 558 pp., ISBN 0-8218-0994-6, $65.00

**[A]**S. Akbulut,*Scharlemann's manifold is standard*, Ann. Math.**149**(2) (1999), 497-510. MR**2000d:57033****[D]**S. Donaldson,*Lefschetz pencils on symplectic manifolds*, J. Diff. Geom. (to appear).**[DK]**S. Donaldson and P. Kronheimer,*Geometry of four-manifolds*, Oxford University Press, 1990. MR**92a:57036****[FQ]**M. Freedman and F. Quinn,*Topology of 4-manifolds*, Princeton Mathematical Series**39**(1990). MR**94b:57021****[FS]**R. Fintushel and R. Stern,*Rational blowdowns of smooth 4-manifolds*, J. Diff. Geom.**46**(1997), 181-235. MR**98j:57047****[F]**T. Fuller,*Diffeomorphism types of genus 2 Lefschetz fibrations*, Math. Ann.**311**(1998), 163-176. MR**99f:57035****[HKK]**J. Harer, A. Kas and R. Kirby,*Handlebody decompositions of complex surfaces*, Memoirs AMS**62**(350) (1986). MR**88e:57030****[Sch]**M. Scharlemann,*Constructing strange manifolds with the dodecahedral space*, Duke Math. Jour.**43**(1976), 33-40. MR**53:6574****[Sma]**S. Smale,*The generalized Poincaré conjecture in higher dimensions*, Bull. Amer. Math. Soc.**66**(1960), 373-375. MR**23:A2220**

Review Information:

Reviewer: Dave Auckly

Affiliation: Kansas State University

Email: dav@math.ksu.edu

Journal: Bull. Amer. Math. Soc.

**38**(2001), 229-234

MSC (2000): Primary 57R65; Secondary 57N13, 53Dxx

Published electronically: December 27, 2000

Review copyright: © Copyright 2000 American Mathematical Society