Title :

Valuations on the character variety: Newton polytopes and Residual Poisson Bracket

Author(s) :

Marché, Julien [Auteur]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Simon, Christopher-Lloyd [Auteur]
Lycée Louis Le Grand
École normale supérieure de Lyon [ENS de Lyon]
Pennsylvania State University [Penn State]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Geometry and Topology

Publisher :

Mathematical Sciences Publishers

Publication date :

2023

ISSN :

1465-3060

English keyword(s) :

Newton polytope
measured lamination
real tree
Goldman Poisson bracket
symplectic structure
skein algebra
Character variety
surface group
valuation

HAL domain(s) :

Mathématiques [math]/Théorie des groupes [math.GR]
Mathématiques [math]/Topologie géométrique [math.GT]
Mathématiques [math]/Algèbres quantiques [math.QA]
Mathématiques [math]/Théorie des représentations [math.RT]

English abstract : [en]

We study the space of measured laminations ML on a closed surface from the valuative point of view. We introduce and study a notion of Newton polytope for an algebraic function on the character variety. We prove for instance ...
Show more >We study the space of measured laminations ML on a closed surface from the valuative point of view. We introduce and study a notion of Newton polytope for an algebraic function on the character variety. We prove for instance that trace functions have unit coefficients at the extremal points of their Newton polytope. Then we provide a definition of tangent space at a valuation and show how the Goldman Poisson bracket on the character variety induces a symplectic structure on this valuative model for ML. Finally we identify this symplectic space with previous constructions due to Thurston and Bonahon.Show less >

Language :

Anglais

Popular science :

Non

Comment :

25 pages, 7 figures

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL