Geodesic
A modular functor from state sums for finite tensor categories and their bimodules
Theory and applications of categories, Tome 38 (2022), pp. 436-594.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We construct a modular functor which takes its values in the monoidal bicategory of finite categories, left exact functors and natural transformations. The modular functor is defined on bordisms that are 2-framed. Accordingly we do not need to require that the finite categories appearing in our construction are semisimple, nor that the finite tensor categories that are assigned to two-dimensional strata are endowed with a pivotal structure. Our prescription can be understood as a state-sum construction. The state-sum variables are assigned to one-dimensional strata and take values in bimodule categories over finite tensor categories, whereby we also account for the presence of boundaries and defects. Our construction allows us to explicitly compute functors associated to surfaces and representations of mapping class groups acting on them.
Publié le :
Classification : 18M20, 18M30, 81T45
Keywords: modular functor, state-sum construction, finite tensor category, monoidal bicategory, mapping class group, factorization, topological defect 
@article{TAC_2022_38_a14,
     author = {J\"urgen Fuchs and Gregor Schaumann and Christoph Schweigert},
     title = {A modular functor from state sums for finite tensor categories and their bimodules},
     journal = {Theory and applications of categories},
     pages = {436--594},
     publisher = {mathdoc},
     volume = {38},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2022_38_a14/}
}
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Jürgen Fuchs; Gregor Schaumann; Christoph Schweigert. A modular functor from state sums for finite tensor categories and their bimodules. Theory and applications of categories, Tome 38 (2022), pp. 436-594. http://geodesic.mathdoc.fr/item/TAC_2022_38_a14/