Harmonic analysis, cohomology, and the large-scale geometry of amenable groups

By Yehuda Shalom. 2004

139 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7aad0f124093a1261cd19aa8fed36ed36f6c192d

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Citations in the corpus

Continuous orbit equivalence rigidity (2015, background): “e will now present explicit constructions of continuous orbit couples out of topological couplings and vice versa. The constructions are really the topological analogues of those in [7, §3] (see also [23] and [20]). 6.1. From topological couplings to continuous orbit couples. Suppose that we are giv”
A SURVEY OF MEASURED GROUP THEORY (2009, unknown): “Consider the Polish space ΛΓ of all maps f : Γ→ Λ with the product uniform topology, and let [Γ,Λ] = { f : Γ→ Λ : f (eΓ) = eΛ} .”
The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidity (2006, unknown): “We note that a new proof was found recently by Shalom [55]; it uses a simpler approach, but it is still far from elementary.”
Orbit Equivalence and Measured Group Theory (2010, methodology): “In geometric group theory, the quasi-isometry invariance of various cohomological properties for amenable groups [Sha04] was obtained that way.”
Homological Invariants and Quasi-Isometry (2003, methodology): “Hence we obtain the following corollary which was known before only under additional finiteness conditions on the groups (see [BrG], [ S ]).”
Coarse differentiation of quasi-isometries I: Spaces not quasi-isometric to Cayley graphs (2006, unknown): “[E, EF, FM1, FM2, FM3, FS, KL, MSW, P1, S1, S2, Sh , W]. For a more detailed discussion of history and motivation, see [EFW1].”
Quasi-isometries and rigidity of solvable groups (2005, methodology): “guments based on the explicit structure of singularities of the spaces studied and cannot apply to polycyclic groups. (6) Shalom has obtained some evidence for the conjecture by cohomological methods [Sh]. For example, Shalom shows that any group quasi-isometric to a polycyclic group has a ﬁnite ind”
Asymptotic Dimension (2007, methodology): “This result was extended to solvable groups [92],[86].”
Ideal bicombings for hyperbolic groups and applications (2003, background): “oups [19]. These elements allow us to argue in analogy with [25]. 1.3. Our interest in Theorem 3 lies ﬁrstly in the attempt to relate more intimately geometric and measurable group theory (as e.g. in [12, 26, 31]). Recall that two countable groups Γ and Λ are called measure equivalent (ME) if there ”
Dimension zero at all scales (2006, background): “ion 0 is ﬁnite and therefore all such groups are coarsely equivalent. To deﬁne asymptotic dimension for an inﬁnitely generated countable group one should consider a left invariant proper metric on it [23]. We describe a natural way to introduce such a metric and prove that any group of asymptotic di”