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1. Link homology


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      Problem 1.1.

      Make $gl(1|1)$-homology concrete and relate it to knot/tangle Floer homology.


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          Problem 1.2.

          Does the superspace coinvariant ring defined as $$\mathbb{C}[x_1,\ldots,x_n,\theta_1,\ldots,\theta_n]\,\big/\,(\mathbb{C}[x_1,\ldots,x_n,\theta_1,\ldots,\theta_n]^{S_n}_+)$$ relate to link homology? What object does $$\mathbb{C}[x_1,\ldots,x_n,\theta_1,\ldots,\theta_n]\,\big/\,(\mathbb{C}[x_1,\ldots,x_n,\theta_1,\ldots,\theta_n]^{S_n}_+)$$ define in the trace of Hecke category?


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              Problem 1.3.

              Do $d$-agonal coinvariants relate to link homology?


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                  Problem 1.4.

                  Do Haiman’s polygraph rings relate to link homology? How do they relate to cables of Hopf link?


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                      Problem 1.5.

                      Do Catalanimal operators appear naturally in link homology?

                          Cite this as: AimPL: Algebra, geometry, and combinatorics of link homology, available at http://aimpl.org/agclinkhom.