Bulletin of the American Mathematical Society

MathSciNet review: 1567161
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).

J. F. Adams and S. B. Priddy, Uniqueness of $B\textrm {SO}$, Math. Proc. Cambridge Philos. Soc. 80 (1976), no. 3, 475–509. MR 431152, DOI 10.1017/S0305004100053111

J. C. Becker and D. H. Gottlieb, The transfer map and fiber bundles, Topology 14 (1975), 1–12. MR 377873, DOI 10.1016/0040-9383(75)90029-4

J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Vol. 347, Springer-Verlag, Berlin-New York, 1973. MR 0420609

Frederick R. Cohen, Thomas J. Lada, and J. Peter May, The homology of iterated loop spaces, Lecture Notes in Mathematics, Vol. 533, Springer-Verlag, Berlin-New York, 1976. MR 0436146

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

John D. S. Jones, The Kervaire invariant of extended power manifolds, Topology 17 (1978), no. 3, 249–266. MR 508888, DOI 10.1016/0040-9383(78)90029-0

Daniel S. Kahn and Stewart B. Priddy, On the transfer in the homology of symmetric groups, Math. Proc. Cambridge Philos. Soc. 83 (1978), no. 1, 91–101. MR 464229, DOI 10.1017/S0305004100054323

Stanley O. Kochman, Homology of the classical groups over the Dyer-Lashof algebra, Trans. Amer. Math. Soc. 185 (1973), 83–136. MR 331386, DOI 10.1090/S0002-9947-1973-0331386-2

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..

I. Madsen, V. Snaith, and J. Tornehave, Infinite loop maps in geometric topology, Math. Proc. Cambridge Philos. Soc. 81 (1977), no. 3, 399–430. MR 494076, DOI 10.1017/S0305004100053482

Mark Mahowald, A new infinite family in ${}_{2}\pi _{*}{}^s$, Topology 16 (1977), no. 3, 249–256. MR 445498, DOI 10.1016/0040-9383(77)90005-2

J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Vol. 347, Springer-Verlag, Berlin-New York, 1973. MR 0420609

J. Peter May, $E_{\infty }$ ring spaces and $E_{\infty }$ ring spectra, Lecture Notes in Mathematics, Vol. 577, Springer-Verlag, Berlin-New York, 1977. With contributions by Frank Quinn, Nigel Ray, and Jørgen Tornehave. MR 0494077

J. P. May, Infinite loop space theory, Bull. Amer. Math. Soc. 83 (1977), no. 4, 456–494. MR 451235, DOI 10.1090/S0002-9904-1977-14318-8

J. P. May, $H_{\infty }$ 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

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

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

J. P. May and R. Thomason, The uniqueness of infinite loop space machines, Topology 17 (1978), no. 3, 205–224. MR 508885, DOI 10.1016/0040-9383(78)90026-5

D. McDuff and G. Segal, Homology fibrations and the “group-completion” theorem, Invent. Math. 31 (1975/76), no. 3, 279–284. MR 402733, DOI 10.1007/BF01403148

Goro Nishida, The nilpotency of elements of the stable homotopy groups of spheres, J. Math. Soc. Japan 25 (1973), 707–732. MR 341485, DOI 10.2969/jmsj/02540707

Daniel Quillen, On the cohomology and $K$-theory of the general linear groups over a finite field, Ann. of Math. (2) 96 (1972), 552–586. MR 315016, DOI 10.2307/1970825

Graeme Segal, Categories and cohomology theories, Topology 13 (1974), 293–312. MR 353298, DOI 10.1016/0040-9383(74)90022-6

James D. Stasheff, Infinite loop spaces—a historical survey, $H$-Spaces (Actes Réunion Neuchâtel, 1970) Lecture Notes in Mathematics, Vol. 196, Springer, Berlin, 1971, pp. 43–53. MR 0281192

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

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

1.

J. F. Adams and S. B. Priddy, Uniqueness of BSO, Math. Proc. Cambridge Philos. Soc. 80 (1976), 475-509. MR 0431152

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