# 3D TQFT and HOMFLYPT homology

@article{Oblomkov20183DTA, title={3D TQFT and HOMFLYPT homology}, author={A. Oblomkov and L. Rozansky}, journal={arXiv: Geometric Topology}, year={2018} }

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… Expand

#### 2 Citations

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