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
- [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
Published electronically:
December 27, 2000
Review copyright:
© Copyright 2000
American Mathematical Society
