0PMA Proposition 33 There is a short split exact sequence of cohomology groups 0\displaystyle 0 →\displaystyle\to ⊕i,j∈ℤ(ℋi,j(D1)⊗ℋk−i,m−j(D2))→ℋk,m(D1⊔D2)→\displaystyle{\mathop{\oplus}\limits_{i,j\in\mathbb{Z}}}({\cal H}^{i,j}(D_{1})\otimes{\cal H}^{k-i,m-j}(D_{2}))\to{\cal H}^{k,m}(D_{1}\sqcup D_{2})\to →\displaystyle\to ⊕i,j∈ℤTor1ℤ(ℋi,j(D1),ℋk−i+1,m−j(D2))→0\displaystyle{\mathop{\oplus}\limits_{i,j\in\mathbb{Z}}}{\mathrm{Tor}}_{1}^{\mathbb{Z}}({\cal H}^{i,j}(D_{1}),{\cal H}^{k-i+1,m-j}(D_{2}))\to 0