Nilpotent quandles (Jacques Darné)

Quandles are algebraic structures which were introduced independendtly by Joyce and by Matveev in 1982 in order to encode invariants of knots and links. They showed in particular that the fundamental quandle is a complete invariant of knots up to mirror image. In this talk, I will introduce a particular class of quandles, called nilpotent. I will explore the basic properties of such quandles and of the invariants that they encode. In particular, I will explain how the language of nilpotent quandles can be used to study invariants of links up to link-homotopy.