Mathematics Colloquia and Seminars

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A dead end in the Cayley graph of a finitely generated group with respect to a particular generating set is an element beyond which a geodesic ray in the Cayley graph from the identity cannot be extended. Dead ends occur in a variety of settings, and occur in different levels of severity, measured by the depth of a dead end. I will describe some aspects of dead end phenonema in several families of groups, including an interesting finitely-presented metabelian group constructed by Baumslag. This last example is used to construct a finitely-presented group with unbounded dead-end depth, in joint work with Tim Riley.