Twists and Gorms and Antifields, oh my!

I define topological twists of supersymmetric field theories in the case when the supercharges involved obey an open'' algebra. Using the Batalin-Vilkovisky field-antifield formalism, I construct twisted theories algorithmically from the supersymmetry data, and explain supersymmetric localisation in terms of anticanonical transformations. I also treat equivariant topological twists and explain how BV observables contain the equivariant cohomology of the space of histories. Some results are generalised to theories with two topological supercharges -- such as the balanced’’ topological field theories of Dijkgraaf and Moore – using the geometry of ``differential gorms’’ of Kochan and Ševera. Finally, I exhibit examples of these constructions, including a $\mathrm{U}(1)$-equivariant topological B-model.