Geodesic
Tropical Fock–Goncharov coordinates for $\mathrm {SL}_3$-webs on surfaces I: construction
Forum of Mathematics, Sigma, Tome 12 (2024)

Voir la notice de l'article provenant de la source Cambridge University Press

For a finite-type surface $\mathfrak {S}$, we study a preferred basis for the commutative algebra $\mathbb {C}[\mathscr {R}_{\mathrm {SL}_3(\mathbb {C})}(\mathfrak {S})]$ of regular functions on the $\mathrm {SL}_3(\mathbb {C})$-character variety, introduced by Sikora–Westbury. These basis elements come from the trace functions associated to certain trivalent graphs embedded in the surface $\mathfrak {S}$. We show that this basis can be naturally indexed by nonnegative integer coordinates, defined by Knutson–Tao rhombus inequalities and modulo 3 congruence conditions. 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. 
@article{10_1017_fms_2023_120,
     author = {Daniel C. Douglas and Zhe Sun},
     title = {Tropical {Fock{\textendash}Goncharov} coordinates for $\mathrm {SL}_3$-webs on surfaces {I:} construction},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {12},
     year = {2024},
     doi = {10.1017/fms.2023.120},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.120/}
}
TY  - JOUR
AU  - Daniel C. Douglas
AU  - Zhe Sun
TI  - Tropical Fock–Goncharov coordinates for $\mathrm {SL}_3$-webs on surfaces I: construction
JO  - Forum of Mathematics, Sigma
PY  - 2024
VL  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.120/
DO  - 10.1017/fms.2023.120
LA  - en
ID  - 10_1017_fms_2023_120
ER  - 
%0 Journal Article
%A Daniel C. Douglas
%A Zhe Sun
%T Tropical Fock–Goncharov coordinates for $\mathrm {SL}_3$-webs on surfaces I: construction
%J Forum of Mathematics, Sigma
%D 2024
%V 12
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.120/
%R 10.1017/fms.2023.120
%G en
%F 10_1017_fms_2023_120
Daniel C. Douglas; Zhe Sun. Tropical Fock–Goncharov coordinates for $\mathrm {SL}_3$-webs on surfaces I: construction. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2023.120

Cité par Sources :