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Homological obstructions to string orientations

Abstract:

We observe that the Poincaré duality isomorphism for a string manifold is an isomorphism of modules over the subalgebra A(2) 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 vani...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1093/imrn/rnq237

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Oxford University Press
Journal:
International Mathematics Research Notices More from this journal
Volume:
2011
Issue:
18
Pages:
4074–4088
Publication date:
2010-11-23
Acceptance date:
2010-09-30
DOI:
EISSN:
1687-0247
ISSN:
1073-7928
Keywords:
Pubs id:
pubs:190655
UUID:
uuid:f6575fac-a821-4c9a-9098-47a126aed3db
Local pid:
pubs:190655
Source identifiers:
190655
Deposit date:
2017-05-08

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