A quasi-isometrically diverse class of bi-orderable solvable and residually finite groups via Taut Dehn spectra

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• Arman Darbinyan, Southampton
• Friday 23 February 2024, 13:45-14:45
• MR13.

If you have a question about this talk, please contact Francesco Fournier-Facio.

In my talk, I will discuss a new invariant, which we call Taut Dehn Spectra, that allows geometric differentiation of finitely generated groups in terms of quasi-isometry. This invariant is a generalization of several previously known quasi-isometry invariants and allows one to construct previously unknown geometrically robust classes of groups. In particular, we will discuss a construction of an uncountable class of pairwise non-quasi-isometric groups that are two-generated, solvable of derived length 3, bi-orderable, and residually finite. In particular, this provides the first example of quasi-isometrically diverse class of bi-orderable groups, and, in addition, recovers or strengthens several known results in this direction that will also be reviewed.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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