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- W1576586546 abstract "We obtain a necessary and sufficient condition for an orientable n-plane bundle 77 over a manifold M” of dimension II = 8k + 1 with k > 1 satisfying certain conditions to have span(q) > 5 or 6. Using a method of least indeterminacy due to Browder when 77 is the tangent bundle and A4 is a spin manifold satisfying w,(M) = 0 and u,,(M) = 0 when k is even, we show that the top-dimensional stable obstruction to the existence to five or six linearly independent vector fields is trivial. We also obtain a variant of the Browder-DuPont invariant which might be a candidate for a new invariant for a spin manifold M. In particular, when dim M = II is congruent to 9 mod 16 and n > 9, if M is 3-connected mod 2 with w,(M) = 0, then span M > 4 implies span M > 6." @default.
- W1576586546 created "2016-06-24" @default.
- W1576586546 creator A5046136567 @default.
- W1576586546 date "1986-02-01" @default.
- W1576586546 modified "2023-10-05" @default.
- W1576586546 title "Vector bundles over (8k+ 3)-dimensional manifolds" @default.
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- W1576586546 doi "https://doi.org/10.2140/pjm.1986.121.427" @default.
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