Multicurves and regular functions on the representation variety of a surface in SU(2) | Zendy

Laurent Charles | Zendy; Julien Marché | Zendy

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Multicurves and regular functions on the representation variety of a surface in SU(2)

Author(s) -

Laurent Charles,

Julien Marché

Publication year - 2012

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.4171/cmh/258

Subject(s) - mathematics , trace (psycholinguistics) , morphism , pure mathematics , surface (topology) , torus , space (punctuation) , representation (politics) , regular representation , action (physics) , algebra over a field , variety (cybernetics) , group (periodic table) , geometry , statistics , politics , political science , law , philosophy , linguistics , chemistry , physics , organic chemistry , quantum mechanics

We consider the representation space of a compact surface, that is the space of morphisms from the fundamental group to SU(2) up to conjugation. We show that the trace functions associated to multicurves on the surface are linearly independent as functions on the representation space. The proof relies on the Fourier decomposition of the trace functions with respect to some torus action provided by a pants decomposition. Consequently the space of trace functions is isomorphic to the skein algebra at A=-1 of the thickened surface.

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