  Building on ideas from [DT98; DS11; Wal17; Hay17], we outline a proposal for
constructing Floer homology groups associated with a G2-manifold. These groups
are generated by associative submanifolds and solutions of the ADHM
Seiberg-Witten equations. The construction is motivated by the analysis of
various transitions which can change the number of associative submanifolds. We
discuss the relation of our proposal to Pandharipande and Thomas' stable pair
invariant of Calabi-Yau 3-folds.
