Event

Jonah Gaster, CIRGET

Friday, April 27, 2018 11:00to12:00
Room PK-5115 , Pavillon President-Kennedy, CA

Coloring curves on surfaces

In the context of proving that the mapping class group has finite asymptotic dimension, Bestivina-Bromberg-Fujiwara exhibited a finite coloring of the curve graph, i.e. a map from the vertices to a finite set so that vertices of distance one have distinct images. In joint work with Josh Greene and Nicholas Vlamis we give more attention to the minimum number of colors needed. We show: The separating curve graph has chromatic number coarsely equal to $g log(g)$, and the subgraph spanned by vertices in a fixed non-zero homology class is uniquely $g-1$-colorable. Time permitting, we discuss related questions, including an intriguing relationship with the Johnson homomorphism of the Torelli group.
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