An infinite torus braid yields a categorified Jones-Wenzl projector

A sequence of Temperley-Lieb algebra elements corresponding to torus braids with growing twisting numbers converges to the Jones-Wenzl projector. We show that a sequence of categorification complexes of these braids also has a limit which may serve as a categorification of the Jones-Wenzl projector.Comment: 23 page

3D TQFT and HOMFLYPT homology

In this note we propose a 3D TQFT such that its Hilbert space on $S^2$, which intersects with defect surfaces along a (possibly self-intersecting) curve $C$ is the HOMFLYPT homology of the link whose diagram is $C$. Previously this homology was interpreted as the space of sections of a special 2-periodic complex of coherent sheaf on $Hilb_n(\mathbb{C}^2)$. TQFT perspective provides a natural explanation for this interpretation, since the category $D^{per}Coh(Hilb_n(\mathbb{C}^2))$ is the Drinfeld center of the two-category of assigned to a point by our TQFT.Comment: 22 pages, 5 figures, comments are welcom

HOMFLYPT homology of Coxeter links

A Coxeter link is a closure of a product of two braids, one being a quasi-Coxeter element and the other being a product of partial full twists. This class of links includes torus knots $T_{n,k}$ and torus links $T_{n,nk}$. We identify the knot homology of a Coxeter link with the space of sections of a particular line bundle on a natural generalization of the punctual locus inside the flag Hilbert scheme of points in $\mathbb{C}^2$.Comment: 23 pages, few misprints are corrected, abstract is expande