pp-adic framed braids II

The Yokonuma–Hecke algebras are quotients of the modular framed braid group and they support Markov traces. In this paper, which is sequel to Juyumaya and Lambropoulou (2007) [6], we explore further the structures of the pp-adic framed braids and the pp-adic Yokonuma–Hecke algebras constructed by Juyumaya and Lambropoulou (2007) [6], by means of dense sub-structures approximating pp-adic elements. We also construct a pp-adic Markov trace on the pp-adic Yokonuma–Hecke algebras and approximate the values of the pp-adic trace on pp-adic elements. Surprisingly, the Markov traces do not re-scale directly to yield isotopy invariants of framed links. This leads to imposing the ‘EE-condition’ on the trace parameters. For solutions of the ‘EE-system’ we then define 2-variable isotopy invariants of modular framed links. These lift to pp-adic isotopy invariants of classical framed links. The Yokonuma–Hecke algebras have topological interpretations in the context of framed knots, of classical knots of singular knots and of transverse knots.