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...

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Bibliographic Details
Published in:Topology and its applications 2007-04, Vol.154 (8), p.1804-1826
Main Authors: Juyumaya, J., Lambropoulou, S.
Format: Article
Language:English
Subjects:
Inverse limits
p-adic framed braids
p-adic infinite cablings
p-adic integers
p-adic Markov traces
p-adic Yokonuma–Hecke algebras
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Summary: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 ) .
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2007.01.010