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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 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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


MathSciNet review: 1567865
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?)

  • General topology and its relations to modern analysis and algebra. , Academic Press, New York-London; Publishing House of the Czechoslovak Academy of Sciences, Prague, 1961. MR 0146784
  • 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, DOI 10.1016/0040-9383(84)90016-8
  • Ronald Brown and Philip J. Higgins, On the connection between the second relative homotopy groups of some related spaces, Proc. London Math. Soc. (3) 36 (1978), no. 2, 193–212. MR 478150, DOI 10.1112/plms/s3-36.2.193
  • Ronald Brown and Philip J. Higgins, On the algebra of cubes, J. Pure Appl. Algebra 21 (1981), no. 3, 233–260. MR 617135, DOI 10.1016/0022-4049(81)90018-9
  • 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, DOI 10.1016/0040-9383(87)90004-8
  • Ronald Brown and Christopher B. Spencer, $G$-groupoids, crossed modules and the fundamental groupoid of a topological group, Nederl. Akad. Wetensch. Proc. Ser. A 79=Indag. Math. 38 (1976), no. 4, 296–302. MR 0419643
  • Ronald Brown and Christopher B. Spencer, Double groupoids and crossed modules, Cahiers Topologie Géom. Différentielle 17 (1976), no. 4, 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, DOI 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, DOI 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, DOI 10.1016/0021-8693(81)90136-8
  • Saunders MacLane 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, DOI 10.1073/pnas.36.1.41
  • 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, DOI 10.1017/S0013091500026766
  • J. H. C. Whitehead, On adding relations to homotopy groups, Ann. of Math. (2) 42 (1941), 409–428. MR 4123, DOI 10.2307/1968907
  • J. H. C. Whitehead, Note on a previous paper entitled “On adding relations to homotopy groups.”, Ann. of Math. (2) 47 (1946), 806–810. MR 17537, DOI 10.2307/1969237
  • J. H. C. Whitehead, Combinatorial homotopy. I, Bull. Amer. Math. Soc. 55 (1949), 213–245. MR 30759, DOI 10.1090/S0002-9904-1949-09175-9
  • J. H. C. Whitehead, Combinatorial homotopy. II, Bull. Amer. Math. Soc. 55 (1949), 453–496. MR 30760, DOI 10.1090/S0002-9904-1949-09213-3
  • J. H. C. Whitehead, Simple homotopy types, Amer. J. Math. 72 (1950), 1–57. MR 35437, DOI 10.2307/2372133
  • J. H. C. Whitehead, A certain exact sequence, Ann. of Math. (2) 52 (1950), 51–110. MR 35997, DOI 10.2307/1969511
  • J. H. C. Whitehead, Algebraic homotopy theory, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, Amer. Math. Soc., Providence, R.I., 1952, pp. 354–357. MR 0045389

  • 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