Selecta Mathematica

, 25:79 | Cite as

Serre duality for Khovanov–Rozansky homology

  • Eugene GorskyEmail author
  • Matthew Hogancamp
  • Anton Mellit
  • Keita Nakagane


We prove that the full twist is a Serre functor in the homotopy category of type A Soergel bimodules. As a consequence, we relate the top and bottom Hochschild degrees in Khovanov–Rozansky homology, categorifying a theorem of Kálmán.

Mathematics Subject Classification

57M25 20C08 18E30 



The authors would like to thank Tamás Kálmán, Andrei Neguț, Alexei Oblomkov and Jacob Rasmussen for the useful discussions. We also thank American Institute of Mathematics, where a part of this work was done, for hospitality. E. G.  was partially supported by the NSF Grants DMS-1700814, DMS-1760329, and the Russian Academic Excellence Project 5-100. M.H.  was supported by NSF Grant DMS-1702274 and also partially supported by NSF Grants DMS-1664240 and DMS-1255334. A.M.  was supported by Austrian Science Fund (FWF) projects Y963-N35 and P-31705. K.N.  was supported by JSPS KAKENHI Grant No. JP19J12350.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Eugene Gorsky
    • 1
    • 2
    Email author
  • Matthew Hogancamp
    • 3
  • Anton Mellit
    • 4
  • Keita Nakagane
    • 5
  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA
  2. 2.International Laboratory of Representation Theory and Mathematical PhysicsNRU-HSEMoscowRussia
  3. 3.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA
  4. 4.Faculty of MathematicsUniversity of ViennaWienAustria
  5. 5.Department of MathematicsTokyo Institute of TechnologyTokyoJapan

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