Book Review
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MathSciNet review:
1567085
Full text of review:
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Book Information:
Author:
Alexander Zabrodsky
Title:
Hopf spaces
Additional book information:
Mathematics Studies, No. 22, North-Holland, Amsterdam, 1976, x + 223 pp., $18.50.
J. F. Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. (2) 72 (1960), 20–104. MR 141119, DOI 10.2307/1970147
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
A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573
Peter Hilton, Guido Mislin, and Joe Roitberg, Localization of nilpotent groups and spaces, North-Holland Mathematics Studies, No. 15, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. MR 0478146
Heinz Hopf, Über die Topologie der Gruppen-Mannigfaltigkeiten und ihre Verallgemeinerungen, Ann. of Math. (2) 42 (1941), 22–52 (German). MR 4784, DOI 10.2307/1968985
J. R. Hubbuck, On homotopy commutative $H$-spaces, Topology 8 (1969), 119–126. MR 238316, DOI 10.1016/0040-9383(69)90004-4
S. Y. Husseini, The topology of classical groups and related topics, Gordon and Breach Science Publishers, New York-London-Paris, 1969. MR 0267601
I. M. James, Bibliography on $H$-spaces, $H$-Spaces (Actes Réunion Neuchâtel, 1970) Lecture Notes in Mathematics, Vol. 196, Springer, Berlin, 1971, pp. 137–156. MR 0281203
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. 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
John Milnor, Construction of universal bundles. II, Ann. of Math. (2) 63 (1956), 430–436. MR 77932, DOI 10.2307/1970012
John W. Milnor and John C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211–264. MR 174052, DOI 10.2307/1970615
Mamoru Mimura, Ronald C. O’Neill, and Hirosi Toda, On $p$-equivalence in the sense of Serre, Jpn. J. Math. 40 (1971), 1–10. MR 305399, DOI 10.4099/jjm1924.40.0_{1}
James Stasheff, $H$-spaces from a homotopy point of view, Lecture Notes in Mathematics, Vol. 161, Springer-Verlag, Berlin-New York, 1970. MR 0270372
15. J. Stasheff, Review of [2] and [9], Math. Reviews 54 (1977), #8623 a, b, 1220-1222.
- 1.
- J. F. Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. (2) 72 (1960), 20-104. MR 0141119
- 2.
- 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
- 3.
- A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Math., vol. 304, Springer-Verlag, Berlin and New York, 1972. MR 365573
- 4.
- P. Hilton, G. Mislin, and J. Roitberg, Localization of nilpotent groups and spaces, Notas de Mathemática, no. 15, North-Holland/American Elsevier, Amsterdam and New York, 1975. MR 478146
- 5.
- H. Hopf, Über die Topologie der Gruppen-Mannigfaltigkeiten und ihre Verallgemeinerungen, Ann. of Math. (2) 42 (1941), 22-52. MR 4784
- 6.
- J. R. Hubbuck, On homotopy commutative H-spaces, Topology 8 (1969), 119-126. MR 238316
- 7.
- S. Y. Husseini, The topology of classical groups and related topics, Gordon and Breach, New York, 1969. MR 267601
- 8.
- I. M. James, Bibliography on H-spaces, Lecture Notes in Math., vol. 196, Springer-Verlag, Berlin and New York, 1971, pp. 137-156. MR 281203
- 9.
- J. P. May, The geometry of iterated loop spaces, Lecture Notes in Math., vol. 271, Springer-Verlag, Berlin and New York, 1972. MR 420610
- 10.
- J. P. May, Infinite loop theory, Bull. Amer. Math. Soc. 83 (1977), 456-494. MR 451235
- 11.
- J. Milnor, Construction of universal bundles. II, Ann. of Math. (2) 63 (1956), 430-436. MR 77932
- 12.
- J. Milnor and J. C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211-264. MR 174052
- 13.
- M. Mimura, R. C. O'Neill, and H. Toda, On p-equivalence in the sense of Serre, Japan J. Math. 40 (1971), 1-10. MR 305399
- 14.
- J. Stasheff, H-spaces from a homotopy point of view, Lecture Notes in Math., vol. 161, Springer-Verlag, Berlin and New York, 1970. MR 270372
- 15.
- J. Stasheff, Review of [2] and [9], Math. Reviews 54 (1977), #8623 a, b, 1220-1222.
Review Information:
Reviewer:
Martin Arkowitz
Journal:
Bull. Amer. Math. Soc.
84 (1978), 929-934
DOI:
https://doi.org/10.1090/S0002-9904-1978-14537-6
