Institut de Mathématiques de Bourgogne

Extriangulated structures from stability conditions and application to braid representations

We use the notion of Bridgeland stability condition and an associated rank function to endow triangulated categories with extriangulated structures and study their extriangulated Grothendieck groups. This study is motivated by Khovanov–Seidel’s categorification of the Burau repre...

Infinite simple characteristic quotients

We construct continuum many infinite, simple, characteristic quotients of non-abelian free groups, answering a 1978 question of James Wiegold. The method is very flexible, allowing to impose certain properties on the quotients, to generalize the construction to large classes of g...