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Homological Obstructions to String Orientations.

Authors :
Douglas, Christopher L.
Henriques, André G.
Hill, Michael A.
Source :
IMRN: International Mathematics Research Notices. Sep2011, Vol. 2011 Issue 18, p4074-4088. 15p.
Publication Year :
2011

Abstract

We observe that the Poincaré duality isomorphism for a string manifold is an isomorphism of modules over the subalgebra of the modulo 2 Steenrod algebra. In particular, the pattern of the operations Sq1, Sq2, and Sq4 on the cohomology of a string manifold has a symmetry around the middle dimension. We characterize this kind of cohomology operation duality in terms of the annihilator of the Thom class of the negative tangent bundle, and in terms of the vanishing of top-degree cohomology operations. We also indicate how the existence of such an operation-preserving duality implies the integrality of certain polynomials in the Pontryagin classes of the manifold. [ABSTRACT FROM PUBLISHER]

Details

Language :
English
ISSN :
10737928
Volume :
2011
Issue :
18
Database :
Academic Search Index
Journal :
IMRN: International Mathematics Research Notices
Publication Type :
Academic Journal
Accession number :
65575052