Book Review
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MathSciNet review:
1567865
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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.
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
- [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 0146784
- [B 1] R. Brown, Some non-Abelian methods in homotopy theory and homological algebra, in Categorical Topology, Proc. Conf. Toledo, Ohio, 1983 (H. L. Bentley, et al., ed.), Heldermann-Verlag, Berlin, 1984, pp. 108-146. MR 785014
- [B 2] R. Brown, Coproducts of crossed P-modules: Applications to second homotopy groups and to the homology of groups, Topology 23 (1984), 337-345. MR 770569
- [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
- [B-H 2] R. Brown and P. J. Higgins, Colimit theorems for relative homotopy groups, J. Pure Appl. Algebra 22 (1981), 11-41. MR 621285
- [B-Hu] R. Brown and J. Huebschmann, Identities among relations, in Low-dimensional Topology (R. Brown and T. L. Thickstun, eds. ), London Math. Soc. Lect. Notes Ser. 46, Cambridge University Press, Cambridge-New York, 1982, pp. 153-202. MR 662431
- [B-L] R. Brown and J.-L. Loday, Van Kampen theorems for diagrams of spaces, Topology 26 (1987), 311-335. MR 899052
- [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.
- [E] G. J. Ellis, Homotopy classification the J. H. C. Whitehead way, Exposition. Math. 6 (1988), 97-110. MR 938178
- [E-S] G. J. Ellis and R. Steiner, Higher-dimensional crossed modules and the homotopy groups of (n + 1)-ads, J. Pure Appl. Algebra 46 (1987), 117-136. MR 897011
- [L] J. L. Loday, Spaces with finitely many non-trivial homotopy groups, J. Pure Appl. Algebra 24 (1982), 179-202. MR 651845
- [Lu] A. S.-T. Lue, Cohomology of groups relative to a variety, J. Algebra 69 (1981), 155-174. MR 613866
- [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
- [P] T. Porter, Extensions, crossed modules and internal categories in categories of groups with operations, Proc. Edinburgh Math. Soc. 30 (1987), 373-381. MR 908444
- [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