issues by choosing a more constrained version of the notion of family, which has a straightforward basis in algebraic geometry, but is somewhat harder to connect to symplectic geometry.

The outcome is an invariant of a symplectic manifold $M$ which depends on the following auxiliary data. Take an element $\lambda$ of the (universal single-variable) Novikov field, and an idempotent $z$ in $\mathit{QH}^0(M)$. To these we associate an appropriate version of the Fukaya category $\mathit{Fuk}(M)_{\lambda,z}$ and its completion (split-closed triangulated envelope) $\mathit{Fuk}(M)_{\lambda,z}^{\mathit{perf}}$. Additionally, choose an elliptic curve $\bar{{\mathscr{S}}}$ over the Novikov field, together with a nonzero algebraic one-form on it. Given a class in odd degree quantum cohomology, $x \in \mathit{QH}^1(M)$, one can then ask whether it is [*periodic*]{}, which means whether objects of the Fukaya category can be extended to families over $\bar{{\mathscr{S}}}$ with deformation behaviour prescribed by $x$. In particular, we can apply this idea to symplectic mapping tori and recover some of the results ordinarily proved using flux. More interestingly, we can exploit existing ideas about the behaviour of Fukaya categories under blowups [@smith10], and thereby arrive at the result stated above. The main point is that the relevant part of the Fukaya category of $B^{\mathit{triv}}$ is well-understood, 