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Book Review

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Book Information

Author(s): A. D. Elmendorf, I. Kriz, M. A. Mandell and J. P. May, M. Cole
Title: Rings, modules, and algebras in stable homotopy theory
Additional book information: Mathematical Surveys and Monographs, no. 47, AMS, Providence, RI, 1997, xi + 249, $62.00, 0-8218-0638-6

Author(s): J. P. May, with contributions by M. Cole, G. Comezaña, S. Costenoble, A. D. Elmendorf, J. P. C. Greenlees, L. G. Lewis, Jr., R. J. Piacenza, G. Triantafillou and S. Waner
Title: Equivariant homotopy and cohomology theory
Additional book information: CBMS Regional Conference Series in Mathematics, no. 91, AMS, Providence, RI, 1996, xiii + 366, $49.00, 0-8128-0319-0

Author(s): J. P. May
Title: A concise course in algebraic topology
Additional book information: Chicago Lectures in Mathematics, The University of Chicago Press, Chicago, IL, 1999, ix + 247, $18.00, 0-226-51183-9 (paper)

References:

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Atiyah, M.F. and Segal, G.B., Equivariant $K$-theory and completion, J. Diff. Geom. 3 (1969), 1-18. MR 41:4575

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Boardman, J.M., Stable homotopy theory, preprint, Warwick University, 1964.

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Brown, E.H., Cohomology theories, Ann. of Math. 75 (1962), 79-85. MR 25:1551

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Brown, E.H. and Peterson, F.P., A spectrum whose $\mathbb{Z}_{p}$cohomology is the algebra of reduced $p$th powers, Topology 5 (1966), 149-156. MR 33:719

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Bruner, R.R., May, J.P., McClure, J.E., Steinberger, M., $H\sb \infty $ring spectra and their applications,, Springer Lecture Notes in Mathematics 1176 (1986), viii+388. MR 88e:55001

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Cohen, F.R., Lada, T.J., May, J.P., The homology of iterated loop spaces, Springer Lecture Notes in Mathematics 533 (1976), vii+490. MR 55:9096

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tom Dieck, T., Bordism of $G$-manifolds and integrality theorems, Topology 9 (1970), 345-384. MR 42:1148

[11]
Elmendorf, A.D., Kriz, I., Mandell, M.A., May, J.P., Modern foundations for stable homotopy theory, Handbook of algebraic topology, North-Holland, Amsterdam, 1995, pp. 213-253. MR 97d:55016

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Hopkins, M.J., Global methods in homotopy theory, Proceedings of the 1985 LMS Symposium on Homotopy Theory, ed. by J.D.S. Jones and E. Rees, 1987, pp. 73-96. MR 89g:55022

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Lewis, L.G., Jr., Is there a convenient category of spectra?, J. Pure and Appl. Alg. 73 (1991), 233-246. MR 92f:55008

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Lewis, L.G., Jr.; May, J.P., Steinberger, M., McClure, J.E., Equivariant stable homotopy theory. With contributions by J. E. McClure, Lecture Notes in Mathematics 1213 (1986), x+538. MR 88e:55002

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Lima, E.L., The Spanier-Whitehead duality in new homotopy categories, Summa Brasil. Math. 4 (1959), 91-148. MR 22:7121

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May, J. P., Stable algebraic topology, 1945-1966, History of Topology, ed. I. M. James, Elsevier, Amsterdam, 1999, pp. 665-723. CMP 2000:04

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May, J.P., Brave new worlds in stable homotopy theory, Homotopy theory via algebraic geometry and group representations (Evanston, IL, 1997) Contemp. Math., 220, Amer. Math. Soc., Providence, RI, 1998, pp. 193-212. MR 99g:55012

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May, J.P. (with contributions by F. Quinn, N. Ray, and J. Tornehave), $E_{\infty }$-ring spaces and $E_{\infty }$-ring spectra, Springer Lecture Notes in Mathematics 577 (1977). MR 58:13008

[19]
Miller, H.R., The Sullivan conjecture on maps from classifying spaces, Ann. of Math. (2) 120 (1984), 39-87. MR 87k:55020

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Milnor, J.W., On the cobordism ring $\Omega ^{*}$ and a complex analogue, Amer. J. Math. 82 (1960), 505-521. MR 22:9975

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Novikov, S.P., The methods of algebraic topology from the viewpoint of cobordism theories, Izv. Akad. Nauk SSSR Ser. Math. 31 (1967), 855-951. MR 36:4561

[22]
Quillen, D.G., On the formal group laws of unoriented and complex cobordism theory, Bull. Amer. Math. Soc. 75 (1969), 1293-1298. MR 40:6565

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Ravenel, D.C., Nilpotence and Periodicity in Stable Homotopy Theory, Annals of Mathematics Studies 128, Princeton University Press, Princeton, NJ, 1992. MR 94b:55015

[24]
Smith, L., On realizing complex cobordism modules, II, Applications to the stable homotopy groups of spheres, Amer. J. Math. 93 (1971), 226-263. MR 43:1186b

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Toda, H., On spectra realizing exterior parts of the Steenrod algebra, Topology 10 (1971), 53-65. MR 42:6814

Additional Information:

Reviewer(s):
John McCleary
Affiliation: Vassar College
Email: mccleary@vassar.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 38 (2001), 245-250.

MSC (2000): Primary 55N20, 55P42, 19L47, 55M35, 55N91, 55P91, 55P92, 55Q91, 55R12, 55R91, 57R85, 55-01, 55N10, 55N15, 55N22, 55P05, 55P20, 55Q05, 55R05, 57M15; Secondary 19D99, 19L99, 55N22, 55T25, 18E30, 55P62, 57S17
DOI: 10.1090/S0273-0979-00-00899-5
PII: S 0273-0979(00)00899-5
Posted: December 27, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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