Annular links, or links in the solid torus, appear across many areas of low-dimensional topology: they can be viewed as braid or tangle closures, representatives for transverse links in the standard contact structure on the three-sphere, or as patterns for satellite constructions, for example.
In 2017, inspired by Ozsváth-Stipsicz-Szabó's construction of the Upsilon invariant in knot Floer homology, Grigsby-Licata-Wehrli introduced annular Rasmussen invariants, by defining an annular filtration on the Khovanov-Lee complex for an annular diagram of a link.
In joint work with Linh Truong, we define an annular filtration on a different complex: Sarkar-Seed-Szabó's perturbation of Szabó's geometric spectral sequence. (I will explain the significance of this triply-filtered complex and its conjectured relationship with some Heegaard Floer invariants.) Our 2D family of annular concordance invariants extend Sarkar-Seed-Szabó's generalized Rasmussen invariants and share many properties with Grigsby-Licata-Wehrli's annular Rasmussen invariants.