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arxiv: 1202.6488 · v4 · pith:SFPTLYCBnew · submitted 2012-02-29 · 🧮 math.GT

Prime component-preservingly amphicheiral link with odd minimal crossing number

classification 🧮 math.GT
keywords knotamphicheiralcrossinglinkminimalnumbercomponent-preservinglyprime
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For every odd integer $c\ge 21$, we raise an example of a prime component-preservingly amphicheiral link with the minimal crossing number $c$. The link has two components, and consists of an unknot and a knot which is $(-)$-amphicheiral with odd minimal crossing number. We call the latter knot a {\it Stoimenow knot}. We also show that the Stoimenow knot is not invertible by the Alexander polynomials.

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