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Ends of groups and related invariants

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If you have a question about this talk, please contact Alexis Marchand.

The number of ends of a group G is an invariant, introduced by Hopf in the 1940s, which encodes the number of ways one can “go to infinity” within G. This notion was later generalised in different ways, by Houghton and by Kropholler and Roller, to study pairs of groups. In this case, one is interested in the geometry of a subgroup embedding and, although the situation becomes more complicated, the number of ends can reveal interesting properties of both the ambient group and the subgroup in question. I will discuss these invariants and various classical results about the structure of groups (or subgroup embeddings) with certain numbers of ends. Time permitting, I will talk about some recent work about group pairs which have two ends in a particularly strong way.

This talk is part of the Junior Geometry Seminar series.

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