Polynomial invariants of graphs on surfaces and virtual knots
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Invariants of Welded Virtual Knots Via Crossed Module Invariants of Knotted Surfaces
We define an invariant of welded virtual knots from each finite crossed module by considering crossed module invariants of ribbon knotted surfaces which are naturally associated with them. We elucidate that the invariants obtained are non-trivial by calculating explicit examples. We define welded virtual graphs and consider invariants of them defined in a similar way. 2000 Mathematics Subject C...
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The VA-polynomial proposed in the author’s earlier paper (Acta Appl. Math. 72 (2002), 295–309) for virtual knots and links is considered in this paper. One goal here is to refine the definition of this polynomial to the case of the ring Z in place of the field Q. Moreover, the approach in the paper mentioned makes it possible to recognize “long virtual knots” obtained from equivalent virtual kn...
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In this paper we define and give examples of a family of polynomial invariants of virtual knots and links. They arise by considering certain 2×2 matrices with entries in a possibly non-commutative ring, for example the quaternions. These polynomials are sufficiently powerful to distinguish the Kishino knot from any classical knot, including the unknot. The contents of the paper are as follows
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تاریخ انتشار 2008