Séminaire Lotharingien de Combinatoire, 78B.38 (2017), 11 pp.

Andrew Timothy Wilson

Torus Link Homology and the Nabla Operator

Abstract. In recent work, Elias and Hogancamp develop a recurrence for the Poincar\'e series of the triply graded Hochschild homology of certain links, one of which is the (n,n) torus link. In this case, Elias and Hogancamp give a combinatorial formula for this homology that is reminiscent of the combinatorics of the modified Macdonald polynomial eigenoperator ∇. We give a combinatorial formula for the homologies of all links considered by Elias and Hogancamp. Our first formula is not easily computable, so we show how to transform it into a computable version. Finally, we conjecture a direct relationship between the (n,n) torus link case of our formula and the symmetric function ∇p1n.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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