Topological field theories on manifolds with Wu structures

Understand

We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2.

• After analysing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf-Witten theories.
• We take a general point of view where the Chern-Simons gauge group and its couplings are encoded in a local system of integral lattices.
• The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action.