most recent 30 from http://mathoverflow.net 2013-05-25T00:03:53Z http://mathoverflow.net/feeds/user/15125 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/65477/actions-orbit-equivalent-to-profinite-ones Alessandro Carderi 2011-05-19T21:56:12Z 2011-05-29T18:11:35Z

<p>Let $G$ be a countable discrete residually finite group.</p> <p>Is there a way to characterise the actions of $G$ that are orbit-equivalent to profinite ones?</p> <p>Ozawa and Popa introduced the concept of weakly compact actions. Weakly compact actions are stable under orbit equivalence and profinite actions are weakly compact.</p> <p>Is it possible to find a weakly compact action that is not orbit equivalent to any profinite action?</p>

http://mathoverflow.net/questions/65045/example-of-an-amenable-finitely-generated-and-presented-group-with-a-non-finitely Alessandro Carderi 2011-05-15T15:18:22Z 2011-05-15T20:43:03Z

<p>I'm looking for an example of a finitely presented and finitely generated amenable group, that has a subgroup which is not finitely generated.</p> <p>The question is easy for finitely generated amenable group and an example is the lamp-lighter group $C_2\wr \mathbb{Z}$. </p> <p>An Abelian and finitely generated group has no such subgroups. There exists a bigger class of groups with this property? </p>

http://mathoverflow.net/questions/82973/the-spectrum-of-dd-for-a-riemannian-manifolds Alessandro Carderi 2011-12-08T15:22:15Z 2011-12-08T15:22:15Z

I known, I would like to know what can happen near $0$. For example, I would like to know if you can have some sort of &quot;spectral gap&quot; and in which cases.

http://mathoverflow.net/questions/65477/actions-orbit-equivalent-to-profinite-ones/65538#65538 Alessandro Carderi 2011-05-20T13:44:58Z 2011-05-20T13:44:58Z

You're right, for non-residually finite groups the question is a kind of stupid. Do you know any counterexample in the residually finite world? I will add the assumption in the question.

http://mathoverflow.net/questions/65477/actions-orbit-equivalent-to-profinite-ones Alessandro Carderi 2011-05-20T12:08:24Z 2011-05-20T12:08:24Z

@Jesse I mean profinite actions of a fixed group $G$. But, if you know some other characterisation, please tell me.

http://mathoverflow.net/questions/65477/actions-orbit-equivalent-to-profinite-ones Alessandro Carderi 2011-05-20T12:02:15Z 2011-05-20T12:02:15Z

Orbit equivalent means that the associated equivalence relations are isomorphic as measured equivalence relations. The profinite actions are projective limits of finite actions. The definition of weakly compact is somehow more technical and if you really want to know the definition, you should check the article of Ozawa and Popa.