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- W2023154127 abstract "Let π i :E i →M , i =1,2, be oriented, smooth vector bundles of rank k over a closed, oriented n -manifold with zero sections s i :M→E i . Suppose that U is an open neighborhood of s 1 ( M ) in E 1 and F :U→E 2 a smooth embedding so that π 2 ∘F∘s 1 :M→M is homotopic to a diffeomorphism f . We show that if k >[( n +1)/2]+1 then E 1 and the induced bundle f ∗ E 2 are isomorphic as oriented bundles provided that f have degree +1; the same conclusion holds if f has degree −1 except in the case where k is even and one of the bundles does not have a nowhere-zero cross-section. For n ≡0(4) and [( n +1)/2]+1< k ⩽ n we give examples of nonisomorphic oriented bundles E 1 and E 2 of rank k over a homotopy n -sphere with total spaces diffeomorphic with orientation preserved, but such that E 1 and f ∗ E 2 are not isomorphic oriented bundles. We obtain similar results and counterexamples in the more difficult limiting case where k =[( n +1)/2]+1 and M is a homotopy n -sphere." @default.
- W2023154127 created "2016-06-24" @default.
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- W2023154127 date "2003-05-01" @default.
- W2023154127 modified "2023-09-27" @default.
- W2023154127 title "Embeddings of the base and bundle isomorphisms" @default.
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- W2023154127 doi "https://doi.org/10.1016/s0166-8641(02)00221-3" @default.
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