An invariant for singular knots

Details An invariant for singular knots An invariant for singular knots

2009-05-22

arxiv.org/abs/0905.3665v2

Mathematics

Geometric Topology

14 pages, 8 figures. To appear in the journal of Knot Theory and its Ramifications

Scientific paper

In this paper we introduce a Jones-type invariant for singular knots, using a Markov trace on the Yokonuma--Hecke algebras ${\rm Y}_{d,n}(u)$ and the theory of singular braids. The Yokonuma--Hecke 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 $SB_n$ into the algebra ${\rm Y}_{d,n}(u)$. 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 ${\rm Y}_{d,n}(u)$.

Affiliated with

Also associated with

No associations

Rating

An invariant for singular knots does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An invariant for singular knots, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An invariant for singular knots will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-325497