Abstract
In this paper we consider the following problem. Let (E, M, N, π) be a differentiable fibre bundle, whereEis the total space,Mthe base space,Nthe fibre, andπ: E→Mthe projection map. Then, given aCrtriangulation (ƒ, D) ofM,can one obtain aCrtriangulation (F, K) ofEsuch that the induced mapƒ–1πF:K→ D is linear? R. Lashof and M. Rothenberg (3) have obtained this result for vector bundles.Using methods quite different from theirs, we obtain a solution in the general case. The methods we use are the geometric methods developed by J. H. C. Whitehead. (7) in his triangulation of differentiable manifolds, as found in (5). In fact, our solution consists of generalizing his techniques in a fibre bundle setting.
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