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Notes on homotopy pull-backs. (English) Zbl 0747.55009

The relationships between M. Mather’s notion of homotopy pullback for homotopy commutative squares [Can. J. Math. 28, 225-263 (1976; Zbl 0351.55005)] and H. J. Baues’ notion for commutative squares [Algebraic homotopy (1989; Zbl 0688.55001)] are investigated. It should be noted that Baues’ book does not contain any reference to Mather’s work. In fact, Baues’ notion seems to be based on investigations by V. Puppe [Manuscr. Math. 12, 113-120 (1974; Zbl 0277.55015)]. New characterizations and properties of the two concepts are given. Interactions with various notions of fibration are studied.
Reviewer: K.H.Kamps (Hagen)

MSC:

55P99 Homotopy theory
55R05 Fiber spaces in algebraic topology
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References:

[1] Baues H. J., Algebraic Homotopy (1989) · doi:10.1017/CBO9780511662522
[2] Dieck T. Tom, Springer Lecture Notes in Math. 157 (1970) · Zbl 0203.25401 · doi:10.1007/BFb0059721
[3] Kieboom R. W., Bull. Soc. Math. Belg. Sér. 32 pp 83– (1980)
[4] Mather M., Can. J. Math 28 pp 225– (1976) · Zbl 0351.55005 · doi:10.4153/CJM-1976-029-0
[5] Puppe V., Manuscripts Math. 12 pp 113– (1974) · Zbl 0277.55015 · doi:10.1007/BF01168646
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