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Two-dimensional topological theories, rational functions and their tensor envelopes

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We study generalized Deligne categories and related tensor envelopes for the universal two-dimensional cobordism theories described by rational functions, recently defined by Sazdanovic and one of the authors.

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Acknowledgements

The authors are grateful to Pavel Etingof for a valuable email discussion. The authors would like to thank Vera Serganova and Noah Snyder for discussions of the Frobenius algebra described in Sect. 5.5 and the referee for many valuable comments and suggestions. M.K. was partially supported by NSF grant DMS-1807425 while working on this paper. Y.K. was partially supported by NSF FRG grant DMS-1564497. The work of V. O. was partially supported by the HSE University Basic Research Program, Russian Academic Excellence Project ’5-100’ and by NSF grant DMS-1702251.

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Authors and Affiliations

  1. Department of Mathematics, Columbia University, New York, NY, 10027, USA

    Mikhail Khovanov & Yakov Kononov

  2. Department of Mathematics, University of Oregon, Eugene, OR, 97403, USA

    Victor Ostrik

  3. Laboratory of Algebraic Geometry, National Research University Higher School of Economics, Moscow, Russia

    Victor Ostrik

  4. Department of Mathematics, Yale University, New Haven, CT, 06511, USA

    Yakov Kononov

  5. Kharkevich Institute for Information Transmission Problems, Moscow, 127994, Russia

    Yakov Kononov

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  1. Mikhail Khovanov
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  2. Victor Ostrik
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  3. Yakov Kononov
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Correspondence to Yakov Kononov.

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Khovanov, M., Ostrik, V. & Kononov, Y. Two-dimensional topological theories, rational functions and their tensor envelopes. Sel. Math. New Ser. 28, 71 (2022). https://doi.org/10.1007/s00029-022-00785-z

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