On the question “Can one hear the shape of a group?” and a Hulanicki type theorem for graphs

@inproceedings{Dudko2018OnTQ,
  title={On the question “Can one hear the shape of a group?” and a Hulanicki type theorem for graphs},
  author={A. Dudko and R. Grigorchuk},
  year={2018}
}
We study the question of whether it is possible to determine a finitely generated group $G$ up to some notion of equivalence from the spectrum $\mathrm{sp}(G)$ 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 $G_\omega$, $\omega\in\{0,1,2\}^\mathbb N$, constructed by the second author in 1984. We show that among them there is a continuum of pairwise non-quasi-isometric groups with $\mathrm{sp}(G_\omega… Expand
5 Citations

Figures from this paper

On spectra and spectral measures of Schreier and Cayley graphs
  • 3
  • PDF
Can one hear the shape of a group
On spectra of representations and graphs. Erratum
  • Highly Influenced
  • PDF
Integrable and Chaotic Systems Associated with Fractal Groups
  • PDF

References

SHOWING 1-10 OF 27 REFERENCES
On the spectrum of the sum of generators for a finitely generated group
  • 94
Spectra of Cayley graphs
  • L. Babai
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. B
  • 1979
  • 149
Amenable groups without finitely presented amenable covers
  • 15
  • PDF
On spectra of Koopman, groupoid and quasi-regular representations
  • 13
  • PDF
Can One Hear the Shape of a Group
  • 3
  • Highly Influential
  • PDF
Degrees of Growth of Finitely Generated Groups, and the Theory of Invariant Means
  • 497
  • Highly Influential
...
1
2
3
...