Categorification conjecture for colored Hopf-link invariants in real projective three-space

Let LL be a Hopf link in RP3\mathbb{R}P^3 whose components are colored by an nn-dimensional skew-symmetric and/or mm-dimensional symmetric representation RR of su(2)su(2). Specialize QbQ_b and QfQ_f to products of monomial factors in qq and tt, and consider the resulting qq-series expansion of ZR(U,Qb,Qf,t,q)Z_{R\emptyset}(U,Q_b,Q_f,t,q). Categorification conjecture. Up to an overall factor, this expansion is the graded Poincaré series of a colored sl(N)sl(N) link homology theory for links in RP3\mathbb{R}P^3. This extends the proposed categorification from the unknot to the computed Hopf-link invariants. The supplied text does not state a resolution status.

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Primary source

John Chae, “Link in RP^3 and the Topological Vertex”, arXiv:2501.12566 (2025).

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