A spherical finite tensor category with a modified trace gives a finite-dimensional open-closed 3d TFT via a new handlebody invariant and the universal construction.
M-traces in (non-unimodular) pivotal categories
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abstract
We generalize the notion of a modified trace (or m-trace) to the setting of non-unimodular categories. M-traces are known to play an important role in low-dimensional topology and representation theory, as well as in studying the category itself. Under mild conditions we give existence and uniqueness results for m-traces in pivotal categories.
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2026 1verdicts
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Non-semisimple open-closed 3d TFT
A spherical finite tensor category with a modified trace gives a finite-dimensional open-closed 3d TFT via a new handlebody invariant and the universal construction.