Reference : Tropical Fock-Goncharov coordinates for SL3-webs on surfaces I: construction
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Physical, chemical, mathematical & earth Sciences : Mathematics
Tropical Fock-Goncharov coordinates for SL3-webs on surfaces I: construction
Sun, Zhe mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Douglas, Daniel C. [Yale University, New Haven CT 06511, U.S.A. > Department of Mathematics]
[en] For a finite-type surface S, we study a preferred basis for the commutative algebra C[XSL3(C)(S)] of regular functions on the SL3(C)-character variety, introduced by Sikora and Westbury. These basis elements come from the trace functions associated to certain tri-valent graphs embedded in the surface S. We show that this basis can be naturally indexed by positive integer coordinates, defined by Knutson-Tao rhombus inequalities. These coordinates are related, by the geometric theory of Fock and Goncharov, to the tropical points at infinity of the dual version of the character variety.
FnR ; FNR13242285 > Zhe Sun > > > 01/09/2018 > 31/08/2020 > 2017

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