7 papers
Nuancing the uniqueness of -rationals
Perrine Jouteur, Olga Paris-Romaskevich, Alexander Thomas
We prove uniqueness of -rational numbers up to conjugacy, using character varieties. Despite the uniqueness, we exhibit a two-parameter family of deformations of rationals with…
Plane geometry of -rationals and Springborn Operations
Perrine Jouteur, Olga Paris-Romaskevich, Alexander Thomas
We study the geometry of -rational numbers, introduced by Morier-Genoud and Ovsienko, for positive real . In particular, we construct and analyse the deformed Farey triangula…
A mirror deformation of Markov numbers
Léa Bittmann, Perrine Jouteur, Ezgi Kantarcı Oğuz +2
We introduce a deformed squared Markov equation given by . Symmetric solutions of this new equation present a remarka…
q-Rationals, link invariants and webs
Perrine Jouteur, Hoel Queffelec
We investigate the role of q-rationals in the context of link invariants. This leads us to introduce and study web categories that q-deform Deligne's categories.
On -deformed Markov numbers. Cohn matrices and perfect matchings with weighted edges
Sam Evans, Perrine Jouteur, Sophie Morier-Genoud +1
We consider a natural -deformation of the classical Markov numbers. This -deformation is closely related to -deformed rational numbers recently introduced by two of us. Bo…
Symmetries of the q-deformed real projective line
Perrine Jouteur
We generalize in two steps the quantized action of the modular group on q-deformed real numbers introduced by Morier-Genoud and Ovsienko. First, we let the projective general linea…
Burau representation of and quantization of the rational projective plane
Perrine Jouteur
The braid group naturally acts on the rational projective plane , this action corresponds to the classical integral reduced Burau representation of…