ScalingStacks

Proposition 39 Let $D$ be a diagram of an oriented $(1,1)$-tangle $L$ and denote by ${\mathrm{cl}}(D)$ the associated diagram of the marked oriented link ${\mathrm{cl}}(L).$ Considering $A$ as a graded $A$-module, we have a canonical isomorphism of cohomology groups (as graded $R$-modules)

$$H^{i}(D,A)\cong H^{i}({\mathrm{cl}}(D)),\hskip 36.135pti\in\mathbb{Z}.$$

(205)