ScalingStacks

Corollary 11 For an oriented link $L$ and integers $i,j$ there are equalities of isomorphism classes of abelian groups

	$\displaystyle{\cal H}^{i,j}(L^{!})\otimes\mathbb{Q}$	$\displaystyle=$	$\displaystyle{\cal H}^{-i,-j}(L)\otimes\mathbb{Q}$		(165)
	$\displaystyle{\mathrm{Tor}}({\cal H}^{i,j}(L^{!}))$	$\displaystyle=$	$\displaystyle{\mathrm{Tor}}({\cal H}^{1-i,-j}(L))$		(166)

where ${\mathrm{Tor}}$ stands for the torsion subgroup.