# Homological obstructions to string orientations

@article{Douglas2008HomologicalOT, title={Homological obstructions to string orientations}, author={Christopher L. Douglas and A C G Henriques and Michael A Hill}, journal={arXiv: Algebraic Topology}, year={2008} }

We observe that the Poincare 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 Sq^1, Sq^2, and Sq^4 on the cohomology of a string manifold has a symmetry around the middle dimension. We characterize this kind of cohomology operation duality in term of the annihilator of the Thom class of the negative tangent bundle, and in terms of the vanishing of top-degree cohomology… CONTINUE READING

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