44 research outputs found
The Haagerup property is stable under graph products
The Haagerup property, which is a strong converse of Kazhdan's property
, has translations and applications in various fields of mathematics such
as representation theory, harmonic analysis, operator K-theory and so on.
Moreover, this group property implies the Baum-Connes conjecture and related
Novikov conjecture. The Haagerup property is not preserved under arbitrary
group extensions and amalgamated free products over infinite groups, but it is
preserved under wreath products and amalgamated free products over finite
groups. In this paper, we show that it is also preserved under graph products.
We moreover give bounds on the equivariant and non-equivariant
-compressions of a graph product in terms of the corresponding
compressions of the vertex groups. Finally, we give an upper bound on the
asymptotic dimension in terms of the asymptotic dimensions of the vertex
groups. This generalizes a result from Dranishnikov on the asymptotic dimension
of right-angled Coxeter groups.Comment: 20 pages, v3 minor change
Conjugacy in Houghton's Groups
Let . Houghton's group is the group of permutations of
, that eventually act as a translation in each
copy of . We prove the solvability of the conjugacy problem and
conjugator search problem for , .Comment: 11 pages, 1 figure, v2 correct typos and fills a small gap in the
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