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Graph products as hierarchically hyperbolic groups

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Daniel Berlyne (CUNY)

Abstract: Direct products and free products are two of the simplest ways of combining groups, yet they still give rise to interesting geometry. Direct products of the integers are commonly realised as lattice points in Euclidean space, while free products of the integers exhibit hyperbolic geometry. What happens when we mix free products with direct products This forms what is known as a graph product, which we show has geometry with both Euclidean and hyperbolic behavior; it is ``hierarchically hyperbolic''. We construct this geometry explicitly, answering two questions of Behrstock, Hagen and Sisto. This is joint work with Jacob Russell.