Displaying similar documents to “Large-scale isoperimetry on locally compact groups and applications”

Vanishing of the first reduced cohomology with values in an L p -representation

Romain Tessera (2009)

Annales de l’institut Fourier

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We prove that the first reduced cohomology with values in a mixing L p -representation, 1 < p < ∞ , vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced ℓ p -cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, the first reduced L p -cohomology on homogeneous, closed at infinity, Riemannian manifolds vanishes....

Følner sequences in polycyclic groups.

Christophe Pittet (1995)

Revista Matemática Iberoamericana

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The isoperimetric inequality |∂Ω| / |Ω| = constant / log |Ω| for finite subsets Ω in a finitely generated group Γ with exponential growth is optimal if Γ is polycyclic.

On the Cantor-Bendixson rank of metabelian groups

Yves Cornulier (2011)

Annales de l’institut Fourier

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We study the Cantor-Bendixson rank of metabelian and virtually metabelian groups in the space of marked groups, and in particular, we exhibit a sequence ( G n ) of 2-generated, finitely presented, virtually metabelian groups of Cantor-Bendixson rank  ω n .

Asymptotic dimension of discrete groups

A. Dranishnikov, J. Smith (2006)

Fundamenta Mathematicae

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We extend Gromov's notion of asymptotic dimension of finitely generated groups to all discrete groups. In particular, we extend the Hurewicz type theorem proven in [B-D2] to general groups. Then we use this extension to prove a formula for the asymptotic dimension of finitely generated solvable groups in terms of their Hirsch length.

Systolic invariants of groups and 2 -complexes via Grushko decomposition

Yuli B. Rudyak, Stéphane Sabourau (2008)

Annales de l’institut Fourier

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We prove a finiteness result for the systolic area of groups. Namely, we show that there are only finitely many possible unfree factors of fundamental groups of  2 -complexes whose systolic area is uniformly bounded. We also show that the number of freely indecomposable such groups grows at least exponentially with the bound on the systolic area. Furthermore, we prove a uniform systolic inequality for all 2 -complexes with unfree fundamental group that improves the previously known bounds...