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).