  We introduce QP manifolds that capture the generalised geometry of type IIA
string backgrounds with Ramond-Ramond fluxes and Romans mass. Each of these is
associated to a BPS brane in type IIA: a D2, D4, or NS5-brane. We explain how
these probe branes are related to their associated QP-manifolds via the AKSZ
topological field theory construction and the recent brane phase space
construction. M-theory/type IIA duality is realised on the QP-manifold side as
symplectic reduction along the M-theory circle (for branes that do not wrap
it); this always produces IIA QP-manifolds with vanishing Romans mass.
