Groups at Infinity and Z-structures

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• Henrique Souza, Universidad Autónoma de Madrid
• Friday 16 May 2025, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Julian Wykowski.

The motto of geometric group theory is to understand a group by means of its geometry – that is, its action on geometric spaces. In geometric spaces that show some form of negative curvature, there is consistently a notion of “boundary” at infinity, be it the Gromov boundary for hyperbolic spaces or the visual boundary for CAT spaces. It is not uncommon for the dynamics of the group action on this boundary to reflect properties of the group, such as its dimension or the existence of certain decompositions. What about general groups? How does one make sense of the “space at infinity”? In this talk, I want to present the notion of a Z-structure which aims to generalize the notion of boundary for a finitely presented group. Introduced by M. Bestvina in the 90’s, this structure encapsulates various properties of the Gromov and visual boundaries while at the same time allowing for more general classes of groups. The main goal of this introductory talk is to illustrate the concept with examples and some of the main results in the theory. Looking forward to seeing everyone there!

This talk is part of the Junior Geometry Seminar series.

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