American Mathematical Society

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 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

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:

Author: William Thurston
Title: Three-dimensional geometry and topology
Additional book information: Princeton Univ. Press, Princeton, NJ, 1997, v+311 pp., ISBN 0-691-08304-5, $39.50$

[An]

M. Anderson, Scalar curvature and geometrization conjectures for $3$ -manifolds, in Comparison Geometry (K. Grove, P. Petersen, eds.), Math. Sci. Res. Ins. Publ. 30, Cambridge University Press, Cambridge, England, 1997. CMP 97:13

[Car]

E. Cartan, Lecons sur la geometrie des espaces de Riemann, Gauthier-Villars, 1928. (1st edition).

Hans Grauert, On Levi’s problem and the imbedding of real-analytic manifolds, Ann. of Math. (2) 68 (1958), 460–472. MR 98847, DOI 10.2307/1970257

R. E. Greene and K. Shiohama, Diffeomorphisms and volume-preserving embeddings of noncompact manifolds, Trans. Amer. Math. Soc. 255 (1979), 403–414. MR 542888, DOI 10.1090/S0002-9947-1979-0542888-3

R. E. Greene and H. Wu, Whitney’s imbedding theorem by solutions of elliptic equations and geometric consequences, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Part 2, Stanford Univ., Stanford, Calif., 1973) Amer. Math. Soc., Providence, R.I., 1975, pp. 287–296. MR 0407908

Richard S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry 17 (1982), no. 2, 255–306. MR 664497

Richard S. Hamilton, The formation of singularities in the Ricci flow, Surveys in differential geometry, Vol. II (Cambridge, MA, 1993) Int. Press, Cambridge, MA, 1995, pp. 7–136. MR 1375255

Shigefumi Mori, Projective manifolds with ample tangent bundles, Ann. of Math. (2) 110 (1979), no. 3, 593–606. MR 554387, DOI 10.2307/1971241

Charles B. Morrey Jr., The analytic embedding of abstract real-analytic manifolds, Ann. of Math. (2) 68 (1958), 159–201. MR 99060, DOI 10.2307/1970048

John G. Ratcliffe, Foundations of hyperbolic manifolds, Graduate Texts in Mathematics, vol. 149, Springer-Verlag, New York, 1994. MR 1299730, DOI 10.1007/978-1-4757-4013-4

Peter Scott, The geometries of $3$-manifolds, Bull. London Math. Soc. 15 (1983), no. 5, 401–487. MR 705527, DOI 10.1112/blms/15.5.401

Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3

Yum Tong Siu and Shing Tung Yau, Compact Kähler manifolds of positive bisectional curvature, Invent. Math. 59 (1980), no. 2, 189–204. MR 577360, DOI 10.1007/BF01390043

Alan Weinstein, On the homotopy type of positively-pinched manifolds, Arch. Math. (Basel) 18 (1967), 523–524. MR 220311, DOI 10.1007/BF01899493

[Wh]

H. Whitney, Differentiable manifolds, Annals of Math. (2) 37 (1936) 809-824.

[WS]

C. Weber and H. Seifert, Die beiden Dodekaederraum, Math. Zeit. 37 (1933) 237-253.

Review Information:

Reviewer: Robert E. Greene
Affiliation: University of California at Los Angeles
Email: greene@math.ucla.edu