An invariant for singular knots

Juyumaya, J; Lambropoulou, S

dc.contributor.author	Juyumaya, J	en
dc.contributor.author	Lambropoulou, S	en
dc.date.accessioned	2014-03-01T02:45:57Z
dc.date.available	2014-03-01T02:45:57Z
dc.date.issued	2009	en
dc.identifier.issn	0218-2165	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/32485
dc.subject	E-condition	en
dc.subject	Markov trace	en
dc.subject	Singular braids	en
dc.subject	Singular knots	en
dc.subject	YokonumaHecke algebra	en
dc.subject.classification	Mathematics	en
dc.subject.other	HECKE ALGEBRA	en
dc.subject.other	BRAIDS	en
dc.title	An invariant for singular knots	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1142/S0218216509007324	en
heal.identifier.secondary	http://dx.doi.org/10.1142/S0218216509007324	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	In this paper we introduce a Jones-type invariant for singular knots, using a Markov trace on the YokonumaHecke algebras Yd,n(u) and the theory of singular braids. The YokonumaHecke algebras have a natural topological interpretation in the context of framed knots. Yet, we show that there is a homomorphism of the singular braid monoid SBn into the algebra Y d,n(u). Surprisingly, the trace does not normalize directly to yield a singular link invariant, so a condition must be imposed on the trace variables. Assuming this condition, the invariant satisfies a skein relation involving singular crossings, which arises from a quadratic relation in the algebra Yd,n(u). © 2009 World Scientific Publishing Company.	en
heal.publisher	WORLD SCIENTIFIC PUBL CO PTE LTD	en
heal.journalName	Journal of Knot Theory and its Ramifications	en
dc.identifier.doi	10.1142/S0218216509007324	en
dc.identifier.isi	ISI:000268123400007	en
dc.identifier.volume	18	en
dc.identifier.issue	6	en
dc.identifier.spage	825	en
dc.identifier.epage	840	en