Rigidity of Fibonacci representations of mapping class groups
Godfard, Pierre1
1 Sorbonne Université, Institut de mathématiques, de Jussieu – Paris Rive Gauche, 4 place Jussieu, 75005 (Paris)
Annales de l'Institut Fourier, Online first, 35 p.

We prove that level 5 Witten–Reshetikhin–Turaev SO(3) quantum representations, also known as the Fibonacci representations, of mapping class groups are locally rigid. More generally, for any prime level ℓ, we prove that the level ℓ SO(3) quantum representations are locally rigid on all surfaces of genus g≥3 if and only if they are locally rigid on surfaces of genus 3 with at most 3 boundary components. This reduces local rigidity in prime level ℓ to a finite number of cases.

Nous démontrons la rigidité locale des représentations quantiques SO(3) de Witten–Reshetikhin–Turaev de niveau 5 des groupes modulaires de surfaces, aussi connues sous le nom de représentations Fibonacci. Plus généralement, pour tout niveau premier ℓ, nous démontrons que les représentations quantiques SO(3) de Witten–Reshetikhin–Turaev de niveau ℓ sont localement rigides pour toutes les surfaces de genre g≥3 si et seulement si elles sont localement rigides pour les surfaces de genre 3 avec au plus 3 composantes de bord. Cela réduit la rigidité en niveau premier ℓ à un nombre fini de cas.

Received:
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Accepted:
Online First:
DOI: 10.5802/aif.3676
Classification: 57R56, 14D07, 14H10
Keywords: Quantum Representations, Mapping Class Groups, Rigidity, TQFT
Mots-clés : Représentations quantiques, groupes modulaires de surfaces, rigidité, TQCT

Godfard, Pierre 1

1 Sorbonne Université, Institut de mathématiques, de Jussieu – Paris Rive Gauche, 4 place Jussieu, 75005 (Paris) 
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Godfard, Pierre. Rigidity of Fibonacci representations of mapping class groups. Annales de l'Institut Fourier, Online first, 35 p.

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