Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


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

Author: H. J. Baues
Title: Algebraic homotopy
Additional book information: Cambridge University Press, Cambridge, New York, 1989, 466 pp., $89.50. ISBN 0-521-33376-8.

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

  • [A] P. Alexandroff, Commemoration of Eduard Čech, General Topology and its Relations to Modern Analysis and Algebra, Proceedings of the Symposium held in Prague, 1961, pp. 29-30. MR 146784
  • Ronald Brown, Some nonabelian methods in homotopy theory and homological algebra, Categorical topology (Toledo, Ohio, 1983) Sigma Ser. Pure Math., vol. 5, Heldermann, Berlin, 1984, pp. 108–146. MR 785014
  • Ronald Brown, Coproducts of crossed 𝑃-modules: applications to second homotopy groups and to the homology of groups, Topology 23 (1984), no. 3, 337–345. MR 770569, https://doi.org/10.1016/0040-9383(84)90016-8
  • [B-H 1] R. Brown and P. J. Higgins, On the connection between the second relative homotopy groups of some related spaces, Proc. London Math. Soc. (3) 36 (1978), 193-212. MR 478150
  • Ronald Brown and Philip J. Higgins, Colimit theorems for relative homotopy groups, J. Pure Appl. Algebra 22 (1981), no. 1, 11–41. MR 621285, https://doi.org/10.1016/0022-4049(81)90080-3
  • R. Brown and J. Huebschmann, Identities among relations, Low-dimensional topology (Bangor, 1979) London Math. Soc. Lecture Note Ser., vol. 48, Cambridge Univ. Press, Cambridge-New York, 1982, pp. 153–202. MR 662431
  • Ronald Brown and Jean-Louis Loday, Van Kampen theorems for diagrams of spaces, Topology 26 (1987), no. 3, 311–335. With an appendix by M. Zisman. MR 899052, https://doi.org/10.1016/0040-9383(87)90004-8
  • [B-S 1] R. Brown and C. B. Spencer, $G$-groupoids, crossed modules, and the fundamental groupoid of a topological group, Proc. Kon. Akad. Wet. 79 (1976), 296-302. MR 419643
  • [B-S 2] R. Brown and C. B. Spencer, Double groupoids and crossed modules, Cahiers Topologie Géom. Différentielle Catégoriques 17 (1976), 343-362. MR 440553
  • [C] E. Čech, Höherdimensionale homotopiegruppen, Verhandlungen des Internationalen Mathematiker-Kongress Zurich, Band 2 (1932), 203.
  • Graham J. Ellis, Homotopy classification the J. H. C. Whitehead way, Exposition. Math. 6 (1988), no. 2, 97–110. MR 938178
  • Graham Ellis and Richard Steiner, Higher-dimensional crossed modules and the homotopy groups of (𝑛+1)-ads, J. Pure Appl. Algebra 46 (1987), no. 2-3, 117–136. MR 897011, https://doi.org/10.1016/0022-4049(87)90089-2
  • Jean-Louis Loday, Spaces with finitely many nontrivial homotopy groups, J. Pure Appl. Algebra 24 (1982), no. 2, 179–202. MR 651845, https://doi.org/10.1016/0022-4049(82)90014-7
  • Abraham S.-T. Lue, Cohomology of groups relative to a variety, J. Algebra 69 (1981), no. 1, 155–174. MR 613866, https://doi.org/10.1016/0021-8693(81)90136-8
  • [M-W] S. Mac Lane and J. H. C. Whitehead, On the 3-type of a complex, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 41-48. MR 33519
  • T. Porter, Extensions, crossed modules and internal categories in categories of groups with operations, Proc. Edinburgh Math. Soc. (2) 30 (1987), no. 3, 373–381. MR 908444, https://doi.org/10.1017/S0013091500026766
  • [W 1] J. H. C. Whitehead, On adding relations to homotopy groups, Ann. of Math. 42 (1941), 409-428. MR 4123
  • [W 2] J. H. C. Whitehead, Note on a previous paper entitled "On adding relations to homotopy groups", Ann. of Math. 47 (1946), 806-810. MR 17537
  • [W 3] J. H. C. Whitehead, Combinatorial homotopy I, Bull. Amer. Math. Soc. 55 (1949), 213-245. MR 30759
  • [W 4] J. H. C. Whitehead, Combinatorial homotopy II, Bull. Amer. Math. Soc. 55 (1949), 453-496. MR 30760
  • [W 5] J. H. C. Whitehead, Simple homotopy types, Amer. J. Math. 72 (1950), 1-57. MR 35437
  • [W 6] J. H. C. Whitehead, A certain exact sequence, Ann. of Math. 52 (1950), 51-110. MR 35997
  • [W 7] J. H. C. Whitehead, Algebraic homotopy theory, Proc. Int. Congress of Mathematicians, Harvard, American Mathematical Society, Providence, Rhode Island, 1952, pp. 354-357. MR 45389

Review Information:

Reviewer: Ronald Brown
Journal: Bull. Amer. Math. Soc. 23 (1990), 182-190
DOI: https://doi.org/10.1090/S0273-0979-1990-15929-4
American Mathematical Society