Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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GEOMETRIC SIMPLICIAL EMBEDDINGS OF ARC-TYPE GRAPHS

  • Received : 2019.06.12
  • Accepted : 2019.12.16
  • Published : 2020.09.01
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Abstract

In this paper, we investigate a family of graphs associated to collections of arcs on surfaces. These multiarc graphs naturally interpolate between arc graphs and flip graphs, both well studied objects in low dimensional geometry and topology. We show a number of rigidity results, namely showing that, under certain complexity conditions, that simplicial maps between them only arise in the "obvious way". We also observe that, again under necessary complexity conditions, subsurface strata are convex. Put together, these results imply that certain simplicial maps always give rise to convex images.

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References

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