1208.1540 (Samuel Monnier)

Canonical quadratic refinements of cohomological pairings from
functorial lifts of the Wu class    [PDF]

Samuel Monnier

We consider categories of manifolds admitting a functorial lift of their Wu class to integral cohomology. We show that the existence of a functorial lift allows to construct canonical quadratic refinements of various pairings defined on the cohomologies of a manifold of dimension 4k+2, of its mapping tori and of manifolds bounded by the latter. We also exhibit the compatibility relations satisfied by these quadratic refinements. This leads in particular to a new Z2-valued topological invariant for spin manifolds of dimension 4k+2 when k = 0,2 or is odd. The motivation for this work comes from the physics of the self-dual field theory in dimension 6, and we explain the use of our results to the study of global gravitational anomaly cancellation involving the self-dual field theory.

View original: http://arxiv.org/abs/1208.1540