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Bilinear pairings on two-dimensional cobordisms and generalizations of the Deligne category

Volume 264 / 2024

Mikhail Khovanov, Radmila Sazdanovic Fundamenta Mathematicae 264 (2024), 1-20 MSC: Primary 18M05; Secondary 18M30, 05A18, 15A63. DOI: 10.4064/fm283-8-2023 Published online: 19 October 2023


The Deligne category of symmetric groups is the additive Karoubi closure of the partition category. It is semisimple for generic values of the parameter $t$ while producing categories of representations of the symmetric group when modded out by the ideal of negligible morphisms when $t$ is a nonnegative integer. The partition category may be interpreted, following Comes, via a particular linearization of the category of two-dimensional oriented cobordisms. The Deligne category and its semisimple quotients admit similar interpretations. This viewpoint coupled to the universal construction of two-dimensional topological theories leads to multi-parameter monoidal generalizations of the partition and the Deligne categories, one for each rational function in one variable.


  • Mikhail KhovanovDepartment of Mathematics
    Columbia University
    New York, NY 10027, USA
  • Radmila SazdanovicDepartment of Mathematics
    North Carolina State University
    Raleigh, NC 27696-8205, USA

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