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arxiv: 1709.08827 · v2 · pith:CKSFHSHKnew · submitted 2017-09-26 · 🧮 math.GT

The structure of a minimal n-chart with two crossings II: Neighbourhoods of Gamma₁cupGamma_(n-1)

classification 🧮 math.GT
keywords gammaalphabetaminimalchartlabelcontainingcrossing
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Given a 2-crossing minimal chart $\Gamma$, a minimal chart with two crossings, set $\alpha=\min\{~i~|~$there exists an edge of label $i$ containing a white vertex$\}$, and $\beta=\max\{~i~|~$there exists an edge of label $i$ containing a white vertex$\}$. In this paper we study the structure of a neighbourhood of $\Gamma_\alpha\cup\Gamma_\beta$, and propose a normal form for 2-crossing minimal $n$-charts, here $\Gamma_\alpha$ and $\Gamma_\beta$ mean the union of all the edges of label $\alpha$ and $\beta$ respectively.

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  1. The linear minimal 4-chart with three crossings

    math.GT 2025-09 unverdicted novelty 5.0

    Any linear minimal 4-chart with three crossings is lor-equivalent to the chart of the 2-twist spun trefoil knot.