INTRODUCTION TO POSITIVE REPRESENTATIONS AND FOCK-GONCHAROV COORDINATES - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2013

INTRODUCTION TO POSITIVE REPRESENTATIONS AND FOCK-GONCHAROV COORDINATES

Frederic Palesi

Résumé

In this notes, we will try to give a simple description of the set of positive representations of the fundamental group of a surface with non-empty boundary to the group PSL m (R), as defined by Fock and Goncharov [1]. The construction uses a special set of coordinates on the space of all representations in PGL m (C) now called the Fock-Goncharov coordinates. For each step of the construction, we will consider the classical cases m = 2 and m = 3 before turning to the general case. We will also give the main property of these representations, namely their faithfulness and discreteness.
Fichier principal
Vignette du fichier
Positive representations v3.pdf (433.69 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01218570 , version 1 (21-10-2015)

Identifiants

  • HAL Id : hal-01218570 , version 1

Citer

Frederic Palesi. INTRODUCTION TO POSITIVE REPRESENTATIONS AND FOCK-GONCHAROV COORDINATES. 2013. ⟨hal-01218570⟩
115 Consultations
845 Téléchargements

Partager

Gmail Facebook X LinkedIn More