Abelian duality in topological field theory
Abelian duality in topological field theory
We prove a topological version of abelian duality where the gauge groups are finite abelian. The theories are finite homotopy TFTs, topological analogues of the $p$-form $U(1)$ gauge theories. Using Brown-Comenetz duality, we extend the duality to finite homotopy TFTs of $\pi$-finite spectra.