Geodesic
Triangulation of Fibre Bundles
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 499-513

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

In this paper we consider the following problem. Let (E, M, N, π) be a differentiable fibre bundle, where E is the total space, M the base space, N the fibre, and π: E → M the projection map. Then, given a Cr triangulation (ƒ, D) of M, can one obtain a Cr triangulation (F, K) of E such that the induced map ƒ–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. 
Putz, H. Triangulation of Fibre Bundles. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 499-513. doi: 10.4153/CJM-1967-042-3
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