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Ex-homotopy theory

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Ex-homotopy theory COMPOSITIO MATHEMATICA M. H. EGGAR Ex-homotopy theory Compositio Mathematica, tome 27, no 2 (1973), p. 185-195. <> © Foundation Compositio Mathematica, 1973, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http:// implique l’accord avec les conditions générales d’utilisation ( Toute utilisation commer- ciale ou impression systématique est constitutive d’une infraction pé- nale. Toute copie ou impression de ce fichier doit contenir la pré- sente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques 185 EX-HOMOTOPY THEORY M. H. Eggar COMPOSITIO MATHEMATICA, Vol. 27. Fasc. 2, 1973, pag. 185-195 Noordhoff International Publishing Printed in the Netherlands The ex-homotopy category has been investigated in recent years by I. M. James, J. Becker, L. Smith, J. F. McClendon, C. A. Robinson and others. In [5 ] I. M. James develops homotopy theory for ex-spaces as far as Puppe sequences, and in [6] he examines the Puppe sequence in a special case in order to calculate ex-homotopy groups. Further developments are hampered by the fact that no sufficiently helpful homology theory for ex-spaces is known. In this paper we obviate the need for one and use results from [2] and [3 ] to derive an EHP-se- quence. The technique is to mimic globally the constructions of ordinary homotopy theory and then to apply comparison theorems to deduce theorems in exhomotopy theory from the corresponding theorems in or- dinary homotopy theory. As an example of our main result we calculate in § 6 some ex-homotopy groups involving the Hopf bundle which, to my knowledge, were not previously obtainable. 1 am most grateful to Professor James for his help and encouragement during the preparation of this work. Throughout the paper we consider only Hausdor

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