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An Adelic Extension of the Jones Polynomial

  • Jesús JuyumayaEmail author
  • Sofia Lambropoulou
Chapter
Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 1)

Abstract

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 Juyumaya and Lambropoulou (Topol. Appl. 154:1804–1826, 2007; arXiv:0905.3626v1, 2009). We further construct an adelic Markov trace, analogous to the p-adic Markov trace constructed in Juyumaya and Lambropoulou (arXiv:0905.3626v1, 2009), and using the traces in Juyumaya (J. Knot Theory Ramif. 13:25–29, 2004) 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.

Keywords

Braid Group Inverse Limit Quadratic Relation Jones Polynomial Oriented Link 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad de Valparaíso Gran BretañaValparaísoChile
  2. 2.Departament of MathematicsNational Technical University of AthensAthensGreece

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