### University of Arkansas Topology Seminar: 3/16/2023

### Speaker: Matthew Clay

### Title: Bounded projections in the *Z*−factor graph II

Let *G* be a free product *G* = *A*_{1} * *A*_{2}* ... * *A*_{k} * *F*_{N} and let *O* be the associated outer space. We show that the diameter of the projection of the subset of *O* where a given element has bounded length to the *Z*−factor graph is bounded. In this talk, we will talk about the tools and techniques that go into the proof. This is joint work with Caglar Uyanik.

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