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Book Review
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Book Information
Author(s):
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:
- [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
- [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
Additional Information:
Reviewer(s):
Ronald
Brown
Review Information:
Journal:
Bull. Amer. Math. Soc.
23
(1990),
182-190.
DOI:
10.1090/S0273-0979-1990-15929-4
PII:
S 0273-0979(1990)15929-4
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