• Corpus ID: 252531714

On Asymptotic and Continuous Group Orlicz Cohomology

  title={On Asymptotic and Continuous Group Orlicz Cohomology},
  author={Yaroslav Kopylov and Emiliano Sequeira},
. We generalize some results on asymptotic and continuous group L p -cohomology to Orlicz cohomology. In particular, we show that asymptotic Orlicz cohomology is a quasi-isometry invariant and that both notions coincide in the case of a locally compact second countable group. The case of degree 1 is studied in more detail. 



On the first Lp-cohomology of discrete groups

For finitely generated groups � , the isomorphism between the firstp -cohomology H 1 .p/ .�/ and the reduced 1-cohomology with coefficients inp .�/ is exploited to obtain vanishing results for H 1

Contracting automorphisms and Lp-cohomology in degree one

We characterize those Lie groups, and algebraic groups over a local field of characteristic zero, whose first reduced Lp-cohomology is zero for all p>1, extending a result of Pansu. As an

The first Lp-cohomology of some finitely generated groups and p-harmonic functions

Some calculations of Orlicz cohomology and Poincar'e–Sobolev–Orlicz inequalities

We carry out calculations of Orlicz cohomology for some basic Riemannian manifolds (the real line, the hyperbolic plane, the ball). Relationship between Orlicz cohomology and

Orlicz spaces and the large scale geometry of Heintze groups

We consider an Orlicz space based cohomology for metric (measured) spaces with bounded geometry. We prove the quasi-isometry invariance for a general Young function. In the hyperbolic case, we prove

Quasi-isometric invariance of continuous group $L^p$-cohomology, and first applications to vanishings

We show that the continuous $L^p$-cohomology of locally compact second countable groups is a quasi-isometric invariant. As an application, we prove partial results supporting a positive answer to a

The lp-Cohomology and the Conformal Dimension of Hyperbolic Cones

For any compact set K⊂RN we construct a hyperbolic graph CK, such that the conformal dimension of CK is at most the box dimension of K.

Non-vanishing for group $L^p$-cohomology of solvable and semisimple Lie groups

We obtain non-vanishing of group $L^p$-cohomology of Lie groups for $p$ large and when the degree is equal to the rank of the group. This applies both to semisimple and to some suitable solvable

Φ-Harmonic functions on discrete groups and the first ℓΦ-cohomology

We study the first cohomology groups of a countable discrete group G with coefficients in a G-module ℓΦ(G), where Φ is an N-function of class Δ2(0) ∩ ▿2(0). Developing the ideas of Puls and

Amenability of Closed Subgroups and Orlicz Spaces

We prove that a closed subgroup $H$ of a second countable locally compact group $G$ is amenable if and only if its left regular representation on an Orlicz space $L^\Phi(G)$ for some