Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

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: J. F. Adams
Title: Infinite loop spaces
Additional book information: Ann. of Math. Studies no. 90, Princeton Univ. Press, Princeton, N. J., 1978, x + 214 pp., $14.00 (cloth), $5.50 (paper).

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

  • 1. J. F. Adams and S. B. Priddy, Uniqueness of BSO, Math. Proc. Cambridge Philos. Soc. 80 (1976), 475-509. MR 431152
  • 2. J. C. Becker and D. H. Gottlieb, The transfer map and fiber bundles, Topology 14 (1975), 1-12. MR 377873
  • 3. J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Math., vol. 347, Springer-Verlag, Berlin and New York, 1973. MR 420609
  • 4. F. R. Cohen, J. P. May, and T. Lada, The homology of iterated loop spaces, Lecture Notes in Math., vol. 533, Springer-Verlag, Berlin and New York, 1976. MR 436146
  • 5. Z. Fiedorowicz and S. B. Priddy, Homology of classical groups over finite fields and their associated infinite loop spaces, Lecture Notes in Math., vol. 674, Springer-Verlag, Berlin and New York, 1978. MR 513424
  • 6. J. D. S. Jones, The Kervaire invariant of extended power manifolds, Topology 17 (1978), 249-266. MR 508888
  • 7. D. S. Kahn and S. B. Priddy, The transfer and stable homotopy theory, Math. Proc. Cambridge Philos. Soc. 83 (1978), 103-111. MR 464230
  • 8. S. O. Kochman, The homology of the classical groups over the Dyer-Lashof algebra, Trans. Amer. Math. Soc. 185 (1973), 83-136. MR 331386
  • 9. I. Madsen and R. J. Milgram, The oriented bordism of topological manifolds and integrality relations, Ann. of Math. Studies. Princeton. (to appear). Univ. Press, Princeton, N. J..
  • 10. I. Madsen, V. P. Snaith, and J. Tornehave, Infinite loop maps in geometric topology, Math. Proc. Cambridge Philos. Soc. 81 (1977), 399-430. MR 494076
  • 11. M. Mahowald, A new infinite famity in ${}\sb{2}\pi\sb {*}{}\sp s$, Topology 16 (1977). 249-256. MR 445498
  • 12. J. P. May, The geometry of iterated loop spaces, Lecture Notes in Math., vol. 271, Springer-Verlag, Berlin and New York, 1972. MR 420610
  • 13. J. P. May (with contributions by F. Quinn, N. Ray, and J. Tornehave), E, Lecture Notes in Math., vol. 577, Springer-Verlag, Berlin and New York, 1977. MR 494077
  • 14. J. P. May, Infinite loop space theory, Bull. Amer. Math. Soc. 83 (1977), 456-494. MR 451235
  • 15. J. P. May, H, Proc. Sympos. Pure Math., vol. 32, Amer. Math. Soc., Providence, R. I., 1978, pp. 229-244. MR 520544
  • 16. J. P. May, Infinite loop space theory revisited, Proc. Conf. Algebra Topology, Waterloo, 1978 (to appear). MR 557188
  • 17. J. P. May, Applications and generalizations of the approximation theorem, Proc. Conf. Algebra Topology, Aarhus, 1978 (to appear). MR 561213
  • 18. J. P. May and R. Thomason, The uniqueness of infinite loop space machines, Topology 17 (1978), 205-224. MR 508885
  • 19. D. McDuff and G. Segal, Homology fibrations and the "group completion" theorem, Invent. Math. 31 (1976), 279-284. MR 402733
  • 20. G. Nishida, The nilpotency of elements of the stable homotopy groups of spheres, J. Math. Soc. Japan 25 (1973), 707-732. MR 341485
  • 21. D. G. Quillen, On the cohomology and K-theory of the general linear groups over a finite field, Ann. of Math. 96 (1972), 552-586. MR 315016
  • 22. G. B. Segal, Categories and cohomology theories, Topology 13 (1974), 293-312. MR 353298
  • 23. J. D. Stasheff, Infinite loop spaces-an historical survey, Lecture Notes in Math., vol. 196, Springer-Verlag, Berlin and New York, 1971, pp. 43-53. MR 281192
  • 24. M. Steinberger, On the equivalence of the two definitions of the algebraic K-theory of a topological space, Proc. Conf. Algebra Topology, Aarhus (to appear). MR 561228
  • 25. F. Waldhausen, Algebraic K-theory of topological spaces. I, Proc. Sympos. Pure Math., vol. 32, Amer. Math. Soc. Providence, R. I., 1978, pp. 35-60. MR 520492

Review Information:

Reviewer: J. P. May
Journal: Bull. Amer. Math. Soc. 1 (1979), 642-646
DOI: https://doi.org/10.1090/S0273-0979-1979-14647-0
American Mathematical Society