Laver's results and low-dimensional topology

Patrick Dehornoy (1, 2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 PPS - Preuves, Programmes et Systèmes

In connection with his interest in selfdistributive algebra, Richard Laver established two deep results with potential applications in low-dimensional topology, namely the existence of what is now known as the Laver tables and the well-foundedness of the standard ordering of positive braids. Here we present these results and discuss the way they could be used in topological applications.

Mots clés: Laver table; selfdistributivity; large cardinal; rack; quandle; link invariant; rack cohomology; R-matrix; set-theoretic Yang-Baxter equation; birack; braid ordering; well-order; unprovability statements; conjugacy problem

Domaines: Topologie géométrique [math.GT]

Patrick Dehornoy. Laver's results and low-dimensional topology. 2014. ⟨hal-00931094⟩