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On the quantum Teichmüller invariants of fibred cusped 3-manifolds

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Abstract

We show that the reduced quantum hyperbolic invariants of pseudo-Anosov diffeomorphisms of punctured surfaces are intertwiners of local representations of the quantum Teichmüller spaces. We characterize them as the only intertwiners that satisfy certain natural cut-and-paste operations of topological quantum field theories and such that their traces define invariants of mapping tori.

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Acknowledgements

We thank the referee for the several suggestions that have helped us to really improve the text.

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Authors and Affiliations

  1. IMAG, Univ Montpellier, CNRS, Montpellier, France

    Stéphane Baseilhac

  2. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy

    Riccardo Benedetti

Authors
  1. Stéphane Baseilhac
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  2. Riccardo Benedetti
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Correspondence to Riccardo Benedetti.

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Baseilhac, S., Benedetti, R. On the quantum Teichmüller invariants of fibred cusped 3-manifolds. Geom Dedicata 197, 1–32 (2018). https://doi.org/10.1007/s10711-017-0315-0

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  • DOI: https://doi.org/10.1007/s10711-017-0315-0

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