  This paper is a companion to the authors' forthcoming work extending Heegaard
Floer theory from closed 3-manifolds to compact 3-manifolds with two boundary
components via quilted Floer cohomology. We describe the first interesting case
of this theory: the invariants of 3-manifolds bounding S^2 union T^2, regarded
as modules over the Fukaya category of the punctured 2-torus. We extract a
short proof of exactness of the Dehn surgery triangle in Heegaard Floer
homology. We show that A-infinity structures on the graded algebra A formed by
the cohomology of two basic objects in the Fukaya category of the punctured
2-torus are governed by just two parameters (m^6,m^8), extracted from the
Hochschild cohomology of A. For the Fukaya category itself, m^6 is nonzero.
