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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2024 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: 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 pp., ISBN 3-7643-6064-X, $69.95$

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

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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

Review Information:

Reviewer: Brayton Gray
Affiliation: University of Illinois at Chicago
Email: brayton@uic.edu
Journal: Bull. Amer. Math. Soc. 38 (2001), 217-220
Published electronically: December 27, 2000
Review copyright: © Copyright 2000 American Mathematical Society