On the computation of torus link homology

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<jats:p>We introduce a new method for computing triply graded link homology, which is particularly well adapted to torus links. Our main application is to the<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0010437X18007571_inline1" /><jats:tex-math>$(n,n)$</jats:tex-math></jats:alternatives></jats:inline-formula>-torus links, for which we give an exact answer for all<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0010437X18007571_inline2" /><jats:tex-math>$n$</jats:tex-math></jats:alternatives></jats:inline-formula>. In several cases, our computations verify conjectures of Gorsky<jats:italic>et al.</jats:italic>relating homology of torus links with Hilbert schemes.</jats:p>

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