Vol. 46, No. 2, 1973

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Attaching Hurewicz fibrations with fiber preserving maps

James Edward Arnold, Jr.

Vol. 46 (1973), No. 2, 325–335

When working with fibrations, there are times when standard topological constructions involving identifications are useful. The problem of course, is to show that identifying fibrations in the proper way yields a fibration. This paper establishes a fairly general result concerning attaching Hurewicz fibrations over a fixed base space with a fiber preserving map. This can be applied to obtain many common topological constructions. In particular a theorem of P. Tulley on mapping cylinders is strengthened, which in turn strengthens the main theorems on strong fiber homotopy equivalence and extensions of fibrations obtained by P. Tulley and S. Langston. In addition, these results are applied to obtain a stronger version of Dold’s pasting lemma, an important step in the construction of classifying spaces for fibrations.

Mathematical Subject Classification
Primary: 55F05
Received: 27 March 1972
Revised: 3 January 1973
Published: 1 June 1973
James Edward Arnold, Jr.