ScalingStacks

Remark 2.2. There is also an equivariant version of $\boldsymbol{\mathrm{Foam}}_{N}$, with facet algebras given by the $\mathrm{GL}(N)$-equivariant cohomology rings $H_{\mathrm{GL}(N)}^{*}(\mathrm{Gr}({\mathbb{C}}^{a}\subset{\mathbb{C}}^{N}))$, defined over the base ring $H_{\mathrm{GL}(N)}^{*}(\mathrm{point})$. This version is important due to its role in the proof of functoriality of Khovanov–Rozansky homology [ETW18] and as the source of Lee-type deformation spectral sequences [Lee05, RW16] and Rasmussen-type invariants [Ras10]. Everything in this paper works, mutatis mutandis, in the equivariant framework.