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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Vector fields on $ RP^m{\times}RP^n$


Author: Donald M. Davis
Journal: Proc. Amer. Math. Soc. 140 (2012), 4381-4388
MSC (2010): Primary 57R25, 55N20
Published electronically: April 18, 2012
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Abstract: The span of a manifold is its maximum number of linearly independent vector fields. We discuss the question, still unresolved, of whether $ \operatorname {span}(P^m\times P^n)$ always equals $ \operatorname {span}(P^m)+\operatorname {span}(P^n)$. Here $ P^n$ denotes real projective space. We use $ BP$-cohomology to obtain new upper bounds for $ \operatorname {span}(P^m\times P^n)$, much stronger than previously known bounds.


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Additional Information

Donald M. Davis
Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
Email: dmd1@lehigh.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11282-1
PII: S 0002-9939(2012)11282-1
Keywords: Vector fields, span, projective space
Received by editor(s): December 16, 2010
Received by editor(s) in revised form: May 31, 2011
Published electronically: April 18, 2012
Communicated by: Brooke Shipley
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.