Simplicial embeddings between multicurve graphs
classification
🧮 math.GT
math.CO
keywords
graphsembeddingsmulticurvesimplicialassociatedcalledcertaincomplex
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We study some graphs associated to a surface, called k-multicurve graphs, which interpolate between the curve complex and the pants graph. Our main result is that, under certain conditions, simplicial embeddings between multicurve graphs are induced by $\pi_1$-injective embeddings of the corresponding surfaces. We also prove the rigidity of the multicurve graphs.
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