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Pré-Publication, Document De Travail Année : 2024

Density and unitarity of the Burau representation from a non-semisimple TQFT

Nathan Geer
  • Fonction : Auteur
Aaron Lauda
  • Fonction : Auteur
Joshua Sussan
  • Fonction : Auteur

Résumé

We study the density of the Burau representation from the perspective of a non-semisimple TQFT at a fourth root of unity. This gives a TQFT construction of Squier's Hermitian form on the Burau representation with possibly mixed signature. We prove that the image of the braid group in the space of possibly indefinite unitary representations is dense. We also argue for the potential applications of non-semisimple TQFTs toward topological quantum computation.
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Dates et versions

hal-04613855 , version 1 (17-06-2024)

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Nathan Geer, Aaron Lauda, Bertrand Patureau-Mirand, Joshua Sussan. Density and unitarity of the Burau representation from a non-semisimple TQFT. 2024. ⟨hal-04613855⟩
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