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On parallelizability and span of the Dold manifolds

Author: Július Korbaš
Journal: Proc. Amer. Math. Soc. 141 (2013), 2933-2939
MSC (2010): Primary 57R25; Secondary 55S40, 57R20
Published electronically: April 30, 2013
MathSciNet review: 3056583
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Abstract: The Dold manifold $ P(m,n)$ is obtained from the product $ S^m \times \mathbb{C}P^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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Additional Information

Július Korbaš
Affiliation: Department of Algebra, Geometry, and Mathematical Education, Faculty of Mathematics, Physics, and Informatics, Comenius University, Mlynská dolina, SK-842 48 Bratislava 4, Slovakia — and — Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava 1, Slovakia

Keywords: Dold manifold, vector field problem, span, stable span, parallelizable manifold, stably parallelizable manifold
Received by editor(s): November 10, 2011
Published electronically: April 30, 2013
Additional Notes: Part of this research was carried out while the author was a member of two research teams supported in part by the grant agency VEGA (Slovakia)
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.