On parallelizability and span of the Dold manifolds

Korbaš, Július

doi:10.1090/S0002-9939-2013-11573-X

On parallelizability and span of the Dold manifolds
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Proc. Amer. Math. Soc. 141 (2013), 2933-2939 Request permission

Abstract:

The Dold manifold $P(m,n)$ is obtained from the product $S^m \times \mathbb CP^n$ of the $m$-dimensional sphere and $n$-dimensional complex projective space by identifying $(x,[z_1, \dots , z_{n+1}])$ with $(-x,[\bar z_1, \dots , \bar z_{n+1}])$, where $\bar z$ denotes the complex conjugate of $z$. We answer the parallelizability question for the Dold manifolds $P(m,n)$ and, by completing an earlier (2008) result due to Peter Novotný, we solve the vector field problem for the manifolds $P(m,1)$.

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