Capitulo de libro
AN ADELIC EXTENSION OF THE JONES POLYNOMIAL
Fecha
2011Registro en:
978-3-642-15636-6
978-3-642-15637-3
1085002
Institución
Resumen
In this paper we represent the classical braids in the Yokonuma--Hecke and the adelic Yokonuma--Hecke algebras. More precisely, we define the completion of the framed braid group and we introduce the adelic Yokonuma--Hecke algebras, in analogy to the p--adic framed braids and the p--adic Yokonuma--Hecke algebras introduced in \cite{jula,jula2}. We further construct an adelic Markov trace, analogous to the p--adic Markov trace constructed in \cite{jula2}, and using the traces in \cite{ju} and the adelic Markov trace we define topological invariants of classical knots and links, upon imposing some condition. Each invariant satisfies a cubic skein relation coming from the Yokonuma--Hecke algebra.