7 papers
Nuancing the unicity of -rationals
Perrine Jouteur, Olga Paris-Romaskevich, Alexander Thomas
We prove unicity of -rational numbers up to conjugacy, using character varieties. Despite the unicity, we exhibit a two-parameter family of deformations of rationals with a modu…
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 OÄuz +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 -deformed real numbers introduced by Morier-Genoud and Ovsienko. First, we let the projective general lin…