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3D TQFT and HOMFLYPT homology

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Abstract

We describe a family of 3d topological B-models whose target spaces are Hilbert schemes of points in \(\mathbb {C}^2\). The interfaces separating theories with different numbers of points correspond to braid strands. The Hilbert space of the picture of a closed braid is the HOMFLY-PT homology of the corresponding link.

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Notes

  1. In the original paper we worked with the affine version of this category of matrix factorizations.

  2. On the picture the red circle is \(S^1\) and the black lines are the defect curve \(C\).

  3. The elements of \(\mathfrak {Br}_n\) are related to the braid graphs by the MOY relations [27].

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Acknowledgements

We would like to thank Dmitry Arinkin, Tudor Dimofte, Eugene Gorsky, Sergey Gukov, Tina Kanstrup, Ivan Losev, Roman Bezrukavnikov and Andrei Neguţ for useful discussions. The authors also extremely grateful to an anonymous referee for many corrections and important suggestion on the structure of the paper. The work of A.O. was supported in part by the NSF CAREER Grant DMS-1352398, NSF FRG Grant DMS-1760373 and Simons Fellowship. The work of L.R. was supported in part by the NSF Grant DMS-1760578. Funding was provided by Simons Foundation (Grant No. 561855), Division of Mathematical Sciences (Grant No. 1108727).

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  1. Department of Mathematics and Statistics, University of Massachusetts at Amherst, Lederle Graduate Research Tower, 710 N. Pleasant Street, Amherst, MA, 01003, USA

    A. Oblomkov

  2. Department of Mathematics, University of North Carolina at Chapel Hill, CB # 3250, Phillips Hall, Chapel Hill, NC, 27599, USA

    L. Rozansky

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Oblomkov, A., Rozansky, L. 3D TQFT and HOMFLYPT homology. Lett Math Phys 113, 71 (2023). https://doi.org/10.1007/s11005-023-01684-w

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  • DOI: https://doi.org/10.1007/s11005-023-01684-w

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