Minimal charts of type (3,3)
Abstract
Let $\Gamma$ be a chart. For each label $m$, we denote by $\Gamma_m$ the "subgraph" of $\Gamma$ consisting of all the edges of label $m$ and their vertices. Let $\Gamma$ be a minimal chart of type $(m;3,3)$. That is, a minimal chart $\Gamma$ has six white vertices, and both of $\Gamma_m\cap\Gamma_{m+1}$ and $\Gamma_{m+1}\cap\Gamma_{m+2}$ consist of three white vertices. Then $\Gamma$ is Cmove equivalent to a minimal chart containing a "subchart" representing a 2twist spun trefoil or its "reflection".
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 arXiv:
 arXiv:1609.08257
 Bibcode:
 2016arXiv160908257N
 Keywords:

 Mathematics  Geometric Topology;
 57Q45 (Primary) 57Q35 (Secondary)
 EPrint:
 28 pages, 23 figures. arXiv admin note: substantial text overlap with arXiv:1603.04639