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Book Review

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Book Information

Author(s): Paul G. Goerss and John F. Jardine
Title: Simplicial homotopy theory
Additional book information: Progress in Mathematics, vol. 174, Birkhauser-Verlag, Basel, 1999, xv + 510, $69.95, ISBN 3-7643-6064-X

References:

[6A]
A. K. Bousfield, E. B. Curtis, D. M. Kan, D. G. Quillen, D. L. Rector, and J. W. Schlesinger, The mod-p lower central series and the Adams spectral sequence, Topology 5 (1966), 331-342. MR 33:8002

[BGM]
M. G. Barratt, V. K. A. M. Gugenheim, and J. C. Moore, On semisimplicial fibre bundles, Am. J. Math. 81 (1959), 639-657. MR 22:1895

[B]
E. H. Brown, Jr., Finite computability of Postnikov complexes, Annl. of Math. 65 (1957), 1-20. MR 18:753a

[C1]
E. B. Curtis, Lower central series of semi-simplicial complexes, Topology 2 (1963), 159-171. MR 27:6267

[C2]
E. B. Curtis, Simplicial Homotopy Theory, Advances in Mathematics 6 (1971), 107-209. MR 43:5529

[EZ]
S. Eilenberg and J. A. Zilber, Semi-simplicial complexes and singular homology, Ann. of Math. 51 (1950), 499-513. MR 11:734e

[K1]
D. M. Kan, On c.s.s. complexes, Amer. J. Math. 79 (1957), 449-476. MR 19:759e

[K2]
D. M. Kan, A combinatorial definition of homotopy groups, Ann. of Math. 67 (1958), 282-312. MR 22:1897

[K3]
D. M. Kan, On homotopy theory and c.s.s. groups, Ann. of Math. 68 (1958), 38-53. MR 22:1898

[Ma]
J. P. May, Simplicial Objects in Algebraic Topology, Van Nostrand Mathematical Studies, no. 11, Van Nostrand, Princeton, NJ, 1967. MR 36:5942

[M1]
J. Milnor, The geometric realization of a semi-simplicial complex, Ann. of Math. 65 (1957), 357-362. MR 18:815d

[M2]
J. Milnor, The construction FK, Princeton, 1956 (mimeographed notes).

[Mo]
J. C. Moore, Seminar on algebraic homotopy theory, Princeton, 1956 (mimeographed notes).

[Qu]
D. G. Quillen, Homotopical Algebra, Lecture Notes in Mathematics, no. 43, Springer-Verlag, New York, 1967. MR 36:6480

Additional Information:

Reviewer(s):
Brayton Gray
Affiliation: University of Illinois at Chicago
Email: brayton@uic.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 38 (2001), 217-220.

MSC (2000): Primary 55-02, 55U10; Secondary 18G30
PII: S 0273-0979(00)00895-8
Posted: December 27, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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