classes containing only two generators, the differential $\partial ^{\infty }$ is trivial. Therefore the resulting homology is $$HF^{+}({Y_{m,n}},\mathfrak{s}_{0}-i\mu _{1}-\mu _{2})={\mathcal{T}^{+}}\oplus {\mathcal{T}^{+}}\;,$$ freely generated by the elements $[\{x_{i-1},b_{1},f_{2}\},j]$ and $[\{x_{i-1},b_{1},f_{1}\},j]$ for $j\geq 0$.

**Class $\mathfrak{s}_{0}$**\
We change the basepoint $z_{1}\in D_{5}$ for a new basepoint $z_{2}\in D_{2}$. By Lemma \[lemaz\], the $\sp $ structure $\mathfrak{s}_{0}-\mu _{2}=\mathfrak{s}_{z_{1}}(\{x_{m-1},b_{2},f_{1}\})$ changes to $\mathfrak{s}_{0}=\mathfrak{s}_{z_{2}}(\{x_{m-1},b_{2},f_{1}\})$. In the new $\sp $ structure we have the same generators as in the $\sp $ structure $\mathfrak{s}_{0}-\mu _{2}$, but with a new relative grading, induced by the basepoint $z_{2}$: $$\xymatrix{ \{u_{2},a_{2},e_{1}\} & \{x_{m-1},b_{2},f_{2}\} \ar@{.>}[d]\\
\{x_{1},c_{1},e_{1}\} \ar@{->}[u] & \{x_{m-1},b_{2},f_{1}\}}$$ From our calculation in the $\sp $ structure $\mathfrak{s}_{0}-\mu _{2}$ we deduce that the only nontrivial differential of $CF^{\infty }$ in this class is $\partial ^{\infty }[\{x_{1},c_{1},e_{1}\},i]=[\{u_{2},a_{2},e_{1}\},i-1]$. In the complex $CF^{+}$ we have $\partial ^{+}[\{x_{1},c_{1},e_{1}\},i]=[\{u_{2},a_{2},e_{1}\},i-1]$ for $i\geq 1$ and $\partial ^{+}[\{x_{1},c_{1},e_{1}\},0]=0$. It follows that

[1]{} & HF\^[+]{}([Y\_[m,n]{}]{},\_[0]{})[\^[+]{}]{}[\^[+]{}]{}\[{x\_[1]{},c\_[1]{},e\_[1]{}},0\],

where the first two summands are freely generated by the elements $[\{x_{m-1},b_{2},f_{2}\},i]$ and $[\{x_{m-1},b_{2},f_{1}\},i]$ for $i\geq 0$. The homology group $HF^{\infty }({Y_{m,n}},\mathfrak{s}_{0})$ however equals $$HF^{\infty }({Y_{m,n}},\mathfrak{s}_{0})\cong {\mathbb{F}}[U,U^{-1}]\oplus {\mathbb{F}}[U,U^{-1}]\,.$$

We have thus calculated the Heegaard–Floer homology $HF^{+}({Y_{m,n}},\mathfrak{s})$ for all torsion $\sp $ structures $\mathfrak{s}$ on the manifold ${Y_{m,n}}$. In the following Subsection, we calculate the absolute gradings 