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 -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.
- [An]
- M. Anderson, Scalar curvature and geometrization conjectures for -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).
- [Gra]
- H. Grauert, On Levi's problem and the imbedding of real analytic manifolds, Ann. of Math. (2) 68 (1958) 460-472. MR 0098847
- [GrS]
- R. E. Greene and K. Shiohama, Diffeomorphisms and volume-preserving embeddings of noncompact manifolds, Trans. Amer. Math. Soc. 255 (1979) 403-414. MR 0542888
- [GrW]
- R. E. Greene and H. Wu, Whitney's embedding theorem for solutions of elliptic equations and geometric consequences, Amer. Math. Soc. Proc. Sym. in Pure Math. 27 (1975) 287-296. MR 0407908
- [Ha]
- R. Hamilton, Three manifolds with positive Ricci curvature, J. Diff. Geom. 17 (1982) 255-306. MR 0664497
- [Ha 2]
- R. Hamilton, The formation of singularities in the Ricci flow, Surveys in Diff. Geom. vol. 1, Intern. Press, 1995. MR 1375255
- [Moi]
- S. Mori, Projective manifolds with ample tangent bundles, Ann. of Math. 110 (1979) 593-606. MR 0554387
- [Mor]
- C. B. Morrey, The analytic embedding of abstract real-analytic manifolds, Ann. of Math. (2) 68 (1958) 159-201. MR 0099060
- [Ra]
- J. G. Ratcliffe, Foundations of Hyperbolic Manifolds, Springer-Verlag, New York, 1994. MR 1299730
- [Sc]
- P. Scott, The geometries of -manifolds, Bull. London Math. Soc. 15 (1983) 401-487. MR 0705527
- [Sw]
- A. Schwarz (Svarc), A volume invariant of coverings, Dokl. Akad. Nauk SSSR 105 (1955) 32-34. MR 17:781d
- [SY]
- Y. T. Siu and S. T. Yau, Compact Kähler manifolds of positive bisectional curvature, Inv. Math. 59 (1980) 189-204. MR 0577360
- [We]
- A. Weinstein, On the homotopy type of positively pinched manifolds, Arch. Math. (Basel) 18 (1967) 523-524. MR 0220311
- [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
Journal:
Bull. Amer. Math. Soc.
35 (1998), 179-188
DOI:
https://doi.org/10.1090/S0273-0979-98-00748-4
Review copyright:
© Copyright 1998
American Mathematical Society