0PM0 Proposition 26 The isomorphism classes of the graded RR-modules Hi(T2,k)H^{i}(T_{2,k}) are given by Hi(T2,k)=0 for i<−k and i>0,H0(T2,k)=R{k}⊕R{k−2},H−1(T2,k)=0,H−2j(T2,k)=(R/2R){4j+k}⊕R{4j−2+k} for 1≤j≤k−12,j∈ℤ,H−2j−1(T2,k)=R{4j+2+k} for 1≤j≤k−12,j∈ℤ,H−k(T2,k)=R{3k}⊕R{3k−2} for even k.\begin{array}[]{lll}H^{i}(T_{2,k})&=&0\hskip 14.45377pt\mbox{ for }i<-k\mbox{ and }i>0,\\ H^{0}(T_{2,k})&=&R\{k\}\oplus R\{k-2\},\\ H^{-1}(T_{2,k})&=&0,\\ H^{-2j}(T_{2,k})&=&(R/2R)\{4j+k\}\oplus R\{4j-2+k\}\hskip 14.45377pt\mbox{ for }1\leq j\leq\frac{k-1}{2},\\ &&j\in\mathbb{Z},\\ H^{-2j-1}(T_{2,k})&=&R\{4j+2+k\}\hskip 14.45377pt\mbox{ for }1\leq j\leq\frac{k-1}{2},j\in\mathbb{Z},\\ H^{-k}(T_{2,k})&=&R\{3k\}\oplus R\{3k-2\}\hskip 14.45377pt\mbox{ for even }k.\end{array}