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Cubical geometry in the polygonalization complex

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Valentina Disarlo (Heidelberg)

The polygonalization complex of a punctured surface is a cube complex
whose vertices correspond to polygonal decompositions of the surface.
Although the complex is not CAT(0), it is contractible and shares many
features of a CAT(0) cube complex. In particular, it has a very rich
family of separating and embedded hyperplanes. We will parametrize it
and characterize its crossing graph via the arc complex. This is a joint
work with M. Bell and R. Tang.