Reference : Singularités orbifoldes de la variété des caractères
Dissertations and theses : Doctoral thesis
Physical, chemical, mathematical & earth Sciences : Mathematics
Singularités orbifoldes de la variété des caractères
[en] Orbifold singularities of the character variety
Guerin, Clément mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
University of Strasbourg, ​Strasbourg, ​​France
Docteur en Mathématiques
Guichard, Olivier mailto
Heusener, Michael mailto
Falbel, Elisha mailto
Lawton, Sean mailto
Souto, Juan mailto
Fock, Vladimir mailto
[en] Character variety ; Orbifold ; Irreducible representations ; Projective representations ; Singularities
[en] In this thesis, we want to understand some singularities in the character variety. In a first chapter, we justify that the characters of irreducible representations from a Fuchsian group to a complex semi-simple Lie group is an orbifold. The orbifold locus is, then, the characters of bad representations. In the second chapter, we focus on the case where the Lie group is PSL(p,C) with p a prime number. In particular we give an explicit description of this locus. In the third and fourth chapter, we describe the isotropy groups (i.e. the centralizers of bad subgroups) arising in the cases when the Lie group is a quotient SL(n,C) (third chapter) and when the Lie group is a quotient of Spin(n,C) in the fourth chapter.
The thesis is entirely written in French. It is available on the usual repository of French Ph.D. Thesis TEL :

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