 Integer-surgery exact triangle in Heegaard Floer homology

For a knot $K$ in an integral homology three-sphere and $n>0$, fix a Spin-c structure ${\mathfrak{t}}_k$ on the $n$-surgery. Write ${\mathfrak{s}}_i$ for structures on zero-surgery with $⟨c_1({\mathfrak{s}}_i),[\hat{F}]⟩=2i$, using a capped Seifert surface. In compatible labels the completed-minus triangle isOne can equally use the plus theory without completing. The first map is the congruence-restricted zero-surgery trace map; the last is the sum of reverse, orientation-reversed $n$-surgery trace maps. The middle map uses a Heegaard triple with an auxiliary lens-space generator. For $n=1$ that lens space is $S^3$, giving the usual three two-ended cobordism maps. For $n>1$ it is important to retain the auxiliary boundary and its fixed Spin-c structure. The U-adic completion of Heegaard Floer homology makes the sums of maps well-defined.