Geodesic
Homotopy Pull-Backs and Applications to Duality
Canadian journal of mathematics, Tome 29 (1977) no. 1, pp. 45-64

Voir la notice de l'article provenant de la source Cambridge University Press

The topic of homotopy pull-backs and push-outs has recently been discussed by a number of authors; Boardman and Vogt [5], Bousfield and Kan [6], Fantham [7], Mather [11], and Vogt [16]. Mather develops the theory with an eye to applications and of particular interest is his cube theorem which appears in this paper as Theorem (1.10); the significance of this theorem to applications is shown in [11]. As often occurs in homotopy theory the dual is not true. The purpose of this paper is to examine approximations to the dual in order to obtain new information concerning classical problems of duality. 
Walker, Marshall. Homotopy Pull-Backs and Applications to Duality. Canadian journal of mathematics, Tome 29 (1977) no. 1, pp. 45-64. doi: 10.4153/CJM-1977-004-3
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