Moore-Tachikawa varieties are certain Hamiltonian holomorphic symplectic conjectured in the context of 2-dimensional topological quantum field theories. We discuss several constructions related to these varieties.

Abstract We prove an extension of the Moore–Schmidt theorem on triviality first cohomology class cocycles for action arbitrary discrete group measure space and with values in compact Hausdorff abelian group. The proof relies a ‘conditional’ Pontryagin duality spaces abstract measurable maps.