Abstract
Let \(X^{k}_{m,n}=\Sigma^{k} (\mathbb{R}\mathbb{P}^{m}/\mathbb{R}\mathbb{P}^{n})\). In this note we completely determine the values of k, m, n for which the total Stiefel–Whitney class w(ξ)=1 for any vector bundle ξ over \(X^{k}_{m,n}\).
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Naolekar, A.C., Thakur, A.S. Vector bundles over iterated suspensions of stunted real projective spaces. Acta Math Hung 142, 339–347 (2014). https://doi.org/10.1007/s10474-013-0343-7
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DOI: https://doi.org/10.1007/s10474-013-0343-7