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Examples of hierarchically hyperbolic groups

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Bruno Robbio (Basque Country & CUNY)

Abstract: Hierarchically hyperbolic groups were recently introduced by J. Behrstock, M. Hagen and A. Sisto in a series of papers [1] and [2]. This class of groups establishes a unified framework to work with groups exhibiting hyperbolic features. The geometric approach that is undertaken in the definition of HHG reflects into strong algebraic and asymptotic properties: HHGs are finitely presented, they satisfy a quadratic isoperimetric inequality and they have finite asymptotic dimension. Moreover, mapping class groups, right angled Artin groups and hyperbolic groups are among the most notorious examples of HHG.
The goal of this talk is to provide a wide range of new examples of HHGs in addition to the classical ones. In order to do this, we will review the basic concepts of the theory and introduce tools that enable the construction of HHG using hyperbolic groups as building blocks.
This talk will include joint work with F. Berlai, as well as with D. Spriano.
[1] J. Behrstock, M. F. Hagen, A. Sisto, Hierarchically hyperbolic spaces I: curve complexes for cubical groups. Geom. Topol. 21 (2017), no. 3, 1731 – 1804;
[2] J. Behrstock, M. F. Hagen, A. Sisto, Hierarchically hyperbolic spaces II: combination theorems and the distance formula. To appear in Pacific J. Math.