Geodesic
Killing rational characteristic classes by surgery
Glasgow mathematical journal, Tome 21 (1980) no. 2, pp. 209-212

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

Let fr:Xr → BO(r) be a sequence of fibrations with maps gr:Xr → Xr+1 such that the usual diagram commutes. For such a situation R. Lashof defines the concept of an X-structure on manifolds (see [3]), and proves a Thom-isomorphism for the cobordism groups of such manifolds. Let n, m be positive integers which are fixed throughout this paper. If r is very big in comparison with n + m then Xr is a simply connected CW-complex and the map (gr)*:H*(Xr; Q)→ H*(Xr+l; Q) is an isomorphism up to dimension n. Let γ be the pull-back over Xr of the universal r-linear bundle (which is, of course, a bundle over BO(r)). If r is very big in comparison with n + m, then we put X = Xr, and we assume that γ is orientable and oriented. The elements of H*(X; Q) of dimension not greater than n, will be called rational universal X-characteristic classes. It is well-known that many of the usual classes of manifolds may be described in terms of X-structures, (e.g. SO, SU, Spin-manifolds etc.). 
Papastavridis, Stavros. Killing rational characteristic classes by surgery. Glasgow mathematical journal, Tome 21 (1980) no. 2, pp. 209-212. doi: 10.1017/S0017089500004389
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