Examples of amalgamated free products and coupling rigidity
نویسندگان
چکیده
منابع مشابه
Free Entropy Dimension in Amalgamated Free Products
We calculate the microstates free entropy dimension of natural generators in an amalgamated free product of certain von Neumann algebras, with amalgamation over a hyperfinite subalgebra. In particular, some ‘exotic’ Popa algebra generators of free group factors are shown to have the expected free entropy dimension. We also show that microstates and non–microstates free entropy dimension agree f...
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We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such an action, which applies for example to surface groups and fundamental groups of surface bundles over S.
متن کاملPositive theories of HNN-extensions and amalgamated free products
It is shown that the positive first-order theory of an HNN-extension G = 〈H, t; tat = φ(a)(a ∈ A)〉 can be reduced to the existential firstorder theory of G provided that A and B are proper subgroups of the base group H with A∩B finite. For an amalgamated free product G = H ∗A J , we show that the positive first-order theory of G can be reduced to the existential first-order theory of G in case ...
متن کامل2 00 9 Amenable actions of amalgamated free products
We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such an action, which applies for example to surface groups and fundamental groups of surface bundles over S.
متن کاملOn Properties of Monoids That Are Modular for Free Products and for Certain Free Products with Amalgamated Submonoids
A property P of string-rewriting systems is called modular if the disjoint union R 1 R 2 of two string-rewriting systems R 1 and R 2 has this property if and only if R 1 and R 2 both have this property. Analogously, a property P of monoids is modular if the free product M 1 M 2 of two monoids M 1 and M 2 has this property if and only if M 1 and M 2 both have this property. Since the string-rewr...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2012
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385711000964