منابع مشابه
On minimal flows, definably amenable groups, and o-minimality
We study definably amenable groups in NIP theories, focusing on the problem raised in [10] of whether weak generic types coincide with almost periodic types, equivalently whether the union of minimal subflows of a suitable type space is closed. We give fairly definitive results in the o-minimal context, including a counterexample.
متن کاملDefinably compact abelian groups
Let M be an o–minimal expansion of a real closed field. Let G be a definably compact definably connected abelian n–dimensional group definable in M. We show the following: the o–minimal fundamental group of G is isomorphic to Z; for each k > 0, the k–torsion subgroup of G is isomorphic to (Z/kZ), and the o–minimal cohomology algebra over Q of G is isomorphic to the exterior algebra over Q with ...
متن کاملAmenable Groups
Throughout we let Γ be a discrete group. For f : Γ → C and each s ∈ Γ we define the left translation action by (s.f)(t) = f(s−1t). Definition 1.1. A group Γ is amenable is there exists a state μ on l∞(Γ) which is invariant under the left translation action: for all s ∈ Γ and f ∈ l∞(Γ), μ(s.f) = μ(f). Example 1.2. Finite groups are amenable: take the state which sends χ{s} to 1 |Γ| for each s ∈ ...
متن کاملGroups, measures, and the NIP
We discuss measures, invariant measures on definable groups, and genericity, often in an NIP (failure of the independence property) environment. We complete the proof of the third author’s conjectures relating definably compact groups G in saturated o-minimal structures to compact Lie groups. We also prove some other structural results about such G, for example the existence of a left invariant...
متن کاملSome extremely amenable groups
A topological group G is extremely amenable if every continuous action of G on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of a Lebesgue space with a non-atomic measure is extremely amenable with the weak topology but not with the uniform one. Strengthening a de la Harpe’s result, we sh...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2018
ISSN: 0894-0347,1088-6834
DOI: 10.1090/jams/896