Geodesic
Torus Link Homology and the Nabla Operator
Séminaire lotharingien de combinatoire, 78B (2017)

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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. 

@article{SLC_2017_78B_a37,
     author = {Andrew Timothy Wilson},
     title = {Torus {Link} {Homology} and the {Nabla} {Operator}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a37/}
}
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AU  - Andrew Timothy Wilson
TI  - Torus Link Homology and the Nabla Operator
JO  - Séminaire lotharingien de combinatoire
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VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a37/
ID  - SLC_2017_78B_a37
ER  - 
%0 Journal Article
%A Andrew Timothy Wilson
%T Torus Link Homology and the Nabla Operator
%J Séminaire lotharingien de combinatoire
%D 2017
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%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a37/
%F SLC_2017_78B_a37
Andrew Timothy Wilson. Torus Link Homology and the Nabla Operator. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a37/