16 research outputs found
Turbulence and Araki-Woods factors
Using Baire category techniques we prove that Araki-Woods factors are not
classifiable by countable structures. As a result, we obtain a far reaching
strengthening as well as a new proof of the well-known theorem of Woods that
the isomorphism problem for ITPFI factors is not smooth. We derive as a
consequence that the odometer actions of Z that preserve the measure class of a
finite non-atomic product measure are not classifiable up to orbit equivalence
by countable structures.Comment: 16 page
Permanence properties of the second nilpotent product of groups
We show that amenability, the Haagerup property, the Kazhdan´s property (T) and exactness are preserved under taking second nilpotent product of groups. We also define the restricted second nilpotent wreath product of groups, this is a semi-direct product akin to the restricted wreath product but constructed from the second nilpotent product. We then show that if two discrete groups have the Haagerup property, the restricted second nilpotent wreath product of them also has the Haagerup property. We finally show that if a discrete group is abelian, then the restricted second nilpotent wreath product constructed from it is unitarizable if and only if the acting group is amenable.Fil: Sasyk, Roman. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin
Borel reducibility and classification of von Neumann algebras
We announce some new results regarding the classification problem for
separable von Neumann algebras. Our results are obtained by applying the notion
of Borel reducibility and Hjorth's theory of turbulence to the isomorphism
relation for separable von Neumann algebras
Uniform bounds for the number of rational points on varieties over global fields
We extend the work of Salberger; Walsh; Castryck, Cluckers, Dittmann and Nguyen; and Vermeulen to prove the uniform dimension growth conjecture of Heath-Brown and Serre for varieties of degree at least 4 over global fields. As an intermediate step, we generalize the bounds of Bombieri and Pila to curves over global fields and in doing so we improve the Bε factor by a log(B) factor.Fil: Paredes, Marcelo Exequiel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Sasyk, Roman. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires; Argentin
Metric approximations of unrestricted wreath products when the acting group is amenable
We give a simple and unified proof showing that the unrestricted wreath product of a weakly sofic, sofic, linear sofic, or hyperlinear group by an amenable group is weakly sofic, sofic, linear sofic, or hyperlinear, respectively. By means of the Kaloujnine-Krasner theorem, this implies that group extensions with amenable quotients preserve the four aforementioned metric approximation properties. We also discuss the case of co-amenable groups.Fil: Brude, Javier Eugenio. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Sasyk, Roman. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin
An ultrapower construction of the multiplier algebra of a C*-algebra with an application to boundary amenability of groups
Using ultrapowers of C-algebras, we provide a new construction of the multiplier algebra of a C-algebra. This extends the work of Avsec and Goldbring [Houston J. Math., to appear, arXiv:1610.09276] to the setting ofnoncommutative and nonseparable C-algebras. We also extend their work to give a new proof of the fact that groups acting transitively on locally finite trees with boundary amenable stabilizers are boundary amenable.Fil: Poggi, Facundo Sebastian. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Sasyk, Roman. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin