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SUMMARY:A quasi-isometrically diverse class of bi-orderable solvable and r
 esidually finite groups via Taut Dehn spectra - Arman Darbinyan\, Southamp
 ton
DTSTART:20240223T134500Z
DTEND:20240223T144500Z
UID:TALK208936@talks.cam.ac.uk
CONTACT:Francesco Fournier-Facio
DESCRIPTION:In my talk\, I will discuss a new invariant\, which we call Ta
 ut Dehn Spectra\, that allows geometric differentiation of finitely genera
 ted groups in terms of quasi-isometry. This invariant is a generalization 
 of several previously known quasi-isometry invariants and allows one to co
 nstruct previously unknown geometrically robust classes of groups. In part
 icular\, we will discuss a construction of an uncountable class of pairwis
 e non-quasi-isometric groups that are two-generated\, solvable of derived 
 length 3\, bi-orderable\, and residually finite. In particular\, this prov
 ides the first example of quasi-isometrically diverse class of bi-orderabl
 e groups\, and\, in addition\, recovers or strengthens several known resul
 ts in this direction that will also be reviewed.
LOCATION:MR13
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