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Book Review

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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?)

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  • 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. Zbigniew Fiedorowicz and Stewart Priddy, Homology of classical groups over finite fields and their associated infinite loop spaces, Lecture Notes in Mathematics, vol. 674, Springer, Berlin, 1978. MR 513424
  • 6. John D. S. Jones, The Kervaire invariant of extended power manifolds, Topology 17 (1978), no. 3, 249–266. MR 508888, https://doi.org/10.1016/0040-9383(78)90029-0
  • 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
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  • 14. J. P. May, Infinite loop space theory, Bull. Amer. Math. Soc. 83 (1977), 456-494. MR 451235
  • 15. J. P. May, 𝐻_{∞} ring spectra and their applications, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 229–243. MR 520544
  • 16. J. P. May, Infinite loop space theory revisited, Algebraic topology, Waterloo, 1978 (Proc. Conf., Univ. Waterloo, Waterloo, Ont., 1978) Lecture Notes in Math., vol. 741, Springer, Berlin, 1979, pp. 625–642. MR 557188
  • 17. J. P. May, Applications and generalizations of the approximation theorem, Algebraic topology, Aarhus 1978 (Proc. Sympos., Univ. Aarhus, Aarhus, 1978), Lecture Notes in Math., vol. 763, Springer, Berlin, 1979, pp. 38–69. MR 561213
  • 18. J. P. May and R. Thomason, The uniqueness of infinite loop space machines, Topology 17 (1978), no. 3, 205–224. MR 508885, https://doi.org/10.1016/0040-9383(78)90026-5
  • 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. Mark Steinberger, On the equivalence of the two definitions of the algebraic 𝐾-theory of a topological space, Algebraic topology, Aarhus 1978 (Proc. Sympos., Univ. Aarhus, Aarhus, 1978), Lecture Notes in Math., vol. 763, Springer, Berlin, 1979, pp. 317–331. MR 561228
  • 25. Friedhelm Waldhausen, Algebraic 𝐾-theory of topological spaces. I, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, 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