Corpus ID: 235458212

Locally compact sofic groups

@inproceedings{Bowen2021LocallyCS,
  title={Locally compact sofic groups},
  author={Lewis Bowen and Peter C. M. Burton},
  year={2021}
}
We introduce the notion of soficity for locally compact groups and list a number of open problems. 

References

SHOWING 1-10 OF 56 REFERENCES
Sofic mean dimension
We introduce mean dimensions for continuous actions of countable sofic groups on compact metrizable spaces. These generalize the Gromov-Lindenstrauss-Weiss mean dimensions for actions of countableExpand
Sofic groups: graph products and graphs of groups
We prove that graph products of sofic groups are sofic, as are graphs of groups for which vertex groups are sofic and edge groups are amenable.
Simple groups without lattices
We show that the group of almost automorphisms of a d-regular tree does not admit lattices. As far as we know, this is the first such example among (compactly generated) simple locally compact groups.
Sofic dimension for discrete measured groupoids
For discrete measured groupoids preserving a probability measure we introduce a notion of sofic dimension that measures the asymptotic growth of the number of sofic approximations on larger andExpand
On sofic approximations of Property (T) groups
We prove Bowen's conjecture that every sequence of finite graphs that locally converges to the Cayley graph of a countably infinite group with Kazhdan Property (T) is essentially a vertex-disjointExpand
Unrestricted wreath products and sofic groups
TLDR
This work shows that the unrestricted wreath product of aSofic group by an amenable group is sofic and exploits the famous Kaloujnine-Krasner theorem and extends, with an additional argument, to hyperlinear-by-amenable groups. Expand
Hyperlinearity, essentially free actions and L2-invariants. The sofic property
Abstract.We prove that Connes’ Embedding Conjecture holds for the von Neumann algebras of sofic groups, that is sofic groups are hyperlinear. Hence we provide some new examples of hyperlinearity. WeExpand
On approximation properties of semidirect products of groups
Let R be a class of groups closed under taking semidirect products with finite kernel and fully residually R-groups. We prove that R contains all R-by-{finitely generated residually finite} groups.Expand
Sofic representations of amenable groups
Using probabilistic methods, Collins and Dykema proved that the free product of two sofic groups amalgamated over a monotileably amenable subgroup is sofic as well. We show that the restriction isExpand
Sofic equivalence relations
We introduce the notion of sofic measurable equivalence relations. Using them we prove that Connes' Embedding Conjecture as well as the Measurable Determinant Conjecture of Luck, Sauer and WegnerExpand
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