group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
A differential integral Wu structure in degree on an oriented smooth manifold is a refinement of the Wu class by a cocycle in degree ordinary differential cohomology , hence a circle (2k-1)-bundle with connection whose underlying higher Dixmier-Douady class equals modulo 2-reduction
These are the characteristic elements of the intersection product on ordinary cohomology/ordinary differential cohomology, inducing its quadratic refinements.
manifold dimension | invariant | quadratic form | quadratic refinement |
---|---|---|---|
signature genus | intersection pairing | integral Wu structure | |
Kervaire invariant | framing |
The following table lists classes of examples of square roots of line bundles
The notion was introduced in def. 2.12 of
motivated by considerations about abelian 7d Chern-Simons theory in
A smooth stack refinement is considered in
Last revised on March 8, 2021 at 17:28:14. See the history of this page for a list of all contributions to it.