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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2024 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
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, $65.00$

References [Enhancements On Off] (What's this?)

[A]
S. Akbulut, Scharlemann's manifold is standard, Ann. Math. 149 (2) (1999), 497-510. MR 1689337
[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 1079726
[FQ]
M. Freedman and F. Quinn, Topology of 4-manifolds, Princeton Mathematical Series 39 (1990). MR 1201584
[FS]
R. Fintushel and R. Stern, Rational blowdowns of smooth 4-manifolds, J. Diff. Geom. 46 (1997), 181-235. MR 1484044
[F]
T. Fuller, Diffeomorphism types of genus 2 Lefschetz fibrations, Math. Ann. 311 (1998), 163-176. MR 1624287
[HKK]
J. Harer, A. Kas and R. Kirby, Handlebody decompositions of complex surfaces, Memoirs AMS 62 (350) (1986). MR 0849942
[Sch]
M. Scharlemann, Constructing strange manifolds with the dodecahedral space, Duke Math. Jour. 43 (1976), 33-40. MR 0402760
[Sma]
S. Smale, The generalized Poincaré conjecture in higher dimensions, Bull. Amer. Math. Soc. 66 (1960), 373-375. MR 0124912

Review Information:

Reviewer: Dave Auckly
Affiliation: Kansas State University
Email: dav@math.ksu.edu
Journal: Bull. Amer. Math. Soc. 38 (2001), 229-234
Published electronically: December 27, 2000
Review copyright: © Copyright 2000 American Mathematical Society