3 citations · 5 across the 7 of their papers we have counts for
8 papers
Profinite rigidity and quandle colourings
Jacques Darn{é}
We show that the numbers of colourings of a link by all finite quandles is equivalent, as an invariant of links, to the profinite completion of the peripheral system. This allows u…
Nilpotent quandles
Jacques Darné, Jacques Darn{é}
A nilpotent quandle is a quandle whose inner automorphism group is nilpotent. Such quandles have been called reductive in previous works, but it turns out that their behaviour is i…
When the lower central series stops: a comprehensive study for braid groups and their relatives
Jacques Darné, Martin Palmer, Arthur Soulié
Understanding the lower central series of a group is, in general, a difficult task. It is, however, a rewarding one: computing the lower central series and the associated Lie algeb…
Braids, inner automorphisms and the Andreadakis problem
Jacques Darné
In this paper, we generalize the tools that were introduced in [Dar19b] in order to study the Andreadakis problem for subgroups of IAn. In particular, we study the behaviour of the…
Milnor invariants of braids and welded braids up to homotopy
Jacques Darné
We consider the group of pure welded braids (also known as loop braids) up to (link-)homotopy. The pure welded braid group classically identifies, via the Artin action, with the gr…
Co-induced actions for topological and filtered groups
Jacques Darné
In this note, we show that the category of strongly central series admits co-induced actions, which means that it is Locally Algebraically Cartesian Closed. We also show that some…