On the TQFT representations of the mapping class groups

1998/04/08 by Louis Funar, Funar, Louis · 1 citation
Mathematics · #20 F 36 #57 N 10 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:10 #msc:20 #msc:36 #msc:57

paper · pdf · doi:10.48550/arxiv.math/9804047

21 pages, 6 eps figures, Latex figures (to appear Pacific.J.Math.)

arxiv created 1998/04/08 · openalex publication_date 1998/04/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the image of the mapping class group by the representations arising in the SU(2)-TQFT is infinite, provided that the genus is bigger than 2 and the level r of the theory is different from 2,3,4,6. In particular the quotient of the mapping class group by the normaizer of the r-th power of a Dehn twist is infinite if the genus is at least 3 and r is bigger than 12.

Citations

• Invariants of 3-manifolds via link polynomials and quantum groups

Cited by

• Abelianization of the SL₂ Hitchin connection at level four

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