nLab Mikhail Khovanov

• website

Selected writings

Introducing Khovanov homology:

• Mikhail Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359-426 [arXiv:math/9908171, doi:10.1215/S0012-7094-00-10131-7, MR1740682 (2002j:57025)]

lecture notes (and on categorification generally):

• Mikhail Khovanov (notes by You Qi), Introduction to categorification, lecture notes, Columbia University (2010, 2020) [web, web, full:pdf]

Review:

• Mikhail Khovanov, Robert Lipshitz, Categorical lifting of the Jones polynomial: a survey, Bulletin (New Series) of the American Mathematical Society (2022) [doi:10.1090/bull/1772]

On braid cobordism and triangulated categories:

• Mikhail Khovanov, Richard Thomas, Braid cobordisms, triangulated categories, and flag varieties, Homology, Homotopy and Applications 9(2007) 19-94 [arXiv:math/0609335, euclid]

Introducing and discussing a cobordism category of “foams” for studying link homology:

• Mikhail Khovanov, $sl(3)$ link homology, Algebr. Geom. Topol. 4 (2004) 1045-1081 [arXiv:math/0304375, doi:10.2140/agt.2004.4.1045]

• Mikhail Khovanov, Louis-Hadrien Robert, Foam evaluation and Kronheimer–Mrowka theories, Advances in Mathematics 376 (2021) 107433 [arXiv:1808.09662, doi:10.1016/j.aim.2020.107433]

• Mikhail Khovanov, Louis-Hadrien Robert, Conical $SL(3)$ foams, Journal of Combinatorial Algebra 6 1/2 (2022) 79-108 [arXiv:2011.11077, doi:10.4171/jca/61]

• Mikhail Khovanov, Universal construction, foams and link homology, lecture series at QFT and Cobordism, CQTS (Mar 2023) [web, video 1:YT]

Discussion of non-deterministic automata as 1-dimensional defect TQFTs:

• Paul Gustafson, Mee Seong Im, Remy Kaldawy, Mikhail Khovanov, Zachary Lihn, Automata and one-dimensional TQFTs with defects [arXiv:2301.00700]

Related entries

• Khovanov homology

category: people