Abstract
In this paper we deflne the p-adic framed braid group F1;n, arising as the inverse limit of the modular framed braids. An element in F1;n can be interpreted geometrically as an inflnite framed cabling. F1;n contains the classical framed braid group as a dense subgroup. This leads to a set of topological generators for F1;n and to approximations for the p-adic framed braids. We also construct a p-adic Yokonuma-Hecke algebra Y1;n(u) as the inverse limit of the classical Yokonuma-Hecke algebras. These are quotients of the modular framed braid groups over a quadratic relation. Finally, we construct on this new algebra a p-adic linear trace that supports the Markov property. Paper presented at the 1017 AMS Meeting.
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