Euler classes of vector bundles over manifolds
Keyword(s):
Abstract Let 𝓔 k denote the set of diffeomorphism classes of closed connected smooth k-manifolds X with the property that for any oriented vector bundle α over X, the Euler class e(α) = 0. We show that if X ∈ 𝓔2n+1 is orientable, then X is a rational homology sphere and π 1(X) is perfect. We also show that 𝓔8 = ∅ and derive additional cohomlogical restrictions on orientable manifolds in 𝓔 k .
2008 ◽
Vol 17
(10)
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pp. 1199-1221
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2007 ◽
Vol 142
(2)
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pp. 259-268
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2005 ◽
Vol 92
(1)
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pp. 99-138
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2004 ◽
Vol 06
(06)
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pp. 833-866
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2019 ◽
Vol 41
(2)
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pp. 553-569
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2019 ◽
pp. 1-38
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2004 ◽
Vol 13
(05)
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pp. 571-585
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