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19 April 2024 |
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Article overview
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3-Dimensional TQFTs from Non-Semisimple Modular Categories | | Marco De Renzi
; Azat M. Gainutdinov
; Nathan Geer
; Bertrand Patureau-Mirand
; Ingo Runkel
; | | Date: |
4 Dec 2019 | | Abstract: | We use modified traces to renormalize Lyubashenko’s closed 3-manifold
invariants coming from twist non-degenerate finite unimodular ribbon
categories. Our construction produces new topological invariants which we
upgrade to 2+1-TQFTs under the additional assumption of factorizability. The
resulting functors provide monoidal extensions of Lyubashenko’s mapping class
group representations, to be discussed in a separate paper. This general
framework encompasses important examples of non-semisimple modular categories
coming from the representation theory of quasi-Hopf algebras, which were left
out of previous non-semisimple TQFT constructions. | | Source: | arXiv, 1912.2063 | | Services: | Forum | Review | PDF | Favorites | |
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