-adic framed braids II

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• 作者：Jesú ; s Juyumaya^a ; ^{juyumaya@uvach.cl} ; Sofia Lambropoulou^b ; ^{sofia@math.ntua.gr} ;
• 关键词：57M27 ; 20F38 ; 20F36 ; 20C08
• 刊名：Advances in Mathematics
• 出版年：2013
• 出版时间：15 February, 2013
• 年：2013
• 卷：234
• 期：Complete
• 页码：149-191
• 全文大小：548 K

文摘

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) , we explore further the structures of the -adic framed braids and the -adic Yokonuma-Hecke algebras constructed by Juyumaya and Lambropoulou (2007) , by means of dense sub-structures approximating -adic elements. We also construct a -adic Markov trace on the -adic Yokonuma-Hecke algebras and approximate the values of the -adic trace on -adic elements. Surprisingly, the Markov traces do not re-scale directly to yield isotopy invariants of framed links. This leads to imposing the ¡®dn.com/content/image/1-s2.0-S0001870812004021-si15.gif""/>-condition¡¯ on the trace parameters. For solutions of the ¡®dn.com/content/image/1-s2.0-S0001870812004021-si16.gif""/>-system¡¯ we then define 2-variable isotopy invariants of modular framed links. These lift to -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.