p-Adic framed braids

In this paper we define the p-adic framed braid group F ∞ , n , arising as the inverse limit of the modular framed braids. An element in F ∞ , n can be interpreted geometrically as an infinite framed cabling. F ∞ , n contains the classical framed braid group as a dense subgroup. This leads to a set of topological generators for F ∞ , n and to approximations for the p-adic framed braids. We further construct a p-adic Yokonuma–Hecke algebra Y ∞ , n ( u ) as the inverse limit of a family of classical Yokonuma–Hecke algebras. These are quotients of the modular framed braid groups over a quadratic relation. Finally, we give topological generators for Y ∞ , n ( u ) .