0PMD Proposition 35 Cohomology groups ℋi,j(T2,k),k>1{\cal H}^{i,j}(T_{2,k}),k>1 are isomorphic to ℋ0,−k(T2,k)=ℤ,ℋ0,2−k(T2,k)=ℤ,ℋ−2j−1,−4j−2−k(T2,k)=ℤ for 1≤j≤k−12,j∈ℤ,ℋ−2j,−4j−k(T2,k)=ℤ2 for 1≤j≤k−12,j∈ℤ,ℋ−2j,−4j+2−k(T2,k)=ℤ for 1≤j≤k−12,j∈ℤ,ℋ−k,−3k(T2,k)=ℤ for even k,ℋ−k,2−3k(T2,k)=ℤ for even k,ℋi,j(T2,k)=0 for all other values of i and j\begin{array}[]{lll}{\cal H}^{0,-k}(T_{2,k})&=&\mathbb{Z},\\ {\cal H}^{0,2-k}(T_{2,k})&=&\mathbb{Z},\\ {\cal H}^{-2j-1,-4j-2-k}(T_{2,k})&=&\mathbb{Z}\hskip 14.45377pt\mbox{ for }1\leq j\leq\frac{k-1}{2},j\in\mathbb{Z},\\ {\cal H}^{-2j,-4j-k}(T_{2,k})&=&\mathbb{Z}_{2}\hskip 14.45377pt\mbox{ for }1\leq j\leq\frac{k-1}{2},j\in\mathbb{Z},\\ {\cal H}^{-2j,-4j+2-k}(T_{2,k})&=&\mathbb{Z}\hskip 14.45377pt\mbox{ for }1\leq j\leq\frac{k-1}{2},j\in\mathbb{Z},\\ {\cal H}^{-k,-3k}(T_{2,k})&=&\mathbb{Z}\hskip 14.45377pt\mbox{ for even }k,\\ {\cal H}^{-k,2-3k}(T_{2,k})&=&\mathbb{Z}\hskip 14.45377pt\mbox{ for even }k,\\ {\cal H}^{i,j}(T_{2,k})&=&0\hskip 14.45377pt\mbox{ for all other values of }i\mbox{ and }j\end{array}