Blog
About

5
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Actions of F_\infty whose II_1 factors and orbit equivalence relations have prescribed fundamental group

      Preprint

      ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          We show that given any subgroup F of R_+ which is either countable or belongs to a certain "large" class of uncountable subgroups, there exist continuously many free ergodic probability measure preserving actions \sigma_i of the free group with infinitely many generators such that their associated group measure space II_1 factors M_i and orbit equivalence relations R_i have fundamental group equal to F and with M_i (respectively R_i) stably non-isomorphic. Moreover, these actions can be taken so that R_i has no outer automorphisms and any automorphism of M_i is unitary conjugate to an automorphism that acts trivially on \(L^\infty(X_i) \subset M_i\).

          Related collections

          Author and article information

          Journal
          2008-03-23
          2008-06-02
          10.1090/S0894-0347-09-00644-4
          0803.3351

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          46L10, 28D15, 46L35, 20E05
          Journal of the American Mathematical Society 23 (2010), 383--403
          1) Minor changes w.r.t. v2. 2) Comment about v2: a modification of our main result provides now the first examples of separable II_1 factors and equivalence relations with uncountable fundamental group different from R_+
          math.OA math.DS

          Algebra

          Comments

          Comment on this article