Artem Dudko: Can one hear the shape of a group?

Előadó: Artem Dudko

Cím: Can one hear the shape of a group?

Absztrakt: I will talk about the joint results with Rostislav Grigorchuk on the question of whether it is possible to determine a finitely generated group G up to some notion of equivalence from the spectrum sp(G) of G. We show that the answer is "No" in a strong sense. As the first example we present the collection of amenable 4-generated groups constructed by Grigorchuk in 1984. We show that among them there is a continuum of pairwise non-quasi-isometric groups with the spectrum consisting of two intervals [-0.5,0] and [0.5,1]. Moreover, for each of these groups there is a continuum of covering groups G with the same spectrum. As the second example we construct a continuum of 2-generated torsion-free step-3 solvable groups with the spectrum [−1,1].