nLab Mikhail Khovanov

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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, Letters in Mathematical Physics 113 (2023), no. 5, Paper No. 93, 38 pp. [arXiv:2301.00700]

• Paul Gustafson, Mee Seong Im, Mikhail Khovanov, Boolean TQFTs with accumulating defects, sofic systems, and automata for infinite words, Letters in Mathematical Physics 114 (2024), no. 6, Paper No. 135, 35 pp. [arXiv:2312.17033]

• Mee Seong Im, Mikhail Khovanov, From finite state automata to tangle cobordisms: a TQFT journey from one to four dimensions, Contemporary Mathematics 817 (2025) 179-220 [arXiv:2309.00708]

Related entries

• Khovanov homology

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