Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 57R25, 55S40, 57R20

Retrieve articles in all journals with MSC (2010): 57R25, 55S40, 57R20


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
Email: korbas@fmph.uniba.sk

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11573-X
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.