Book Review

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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

**[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**

Review Information:

Reviewer: Brayton Gray

Affiliation: University of Illinois at Chicago

Email: brayton@uic.edu

Journal: Bull. Amer. Math. Soc.

**38**(2001), 217-220

MSC (2000): Primary 55-02, 55U10; Secondary 18G30

Published electronically: December 27, 2000

Review copyright: © Copyright 2000 American Mathematical Society