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Convex structures revisited

Published online by Cambridge University Press:  09 January 2015

LIVIU PĂUNESCU
LIVIU PĂUNESCU*
Affiliation:
Institute of Mathematics ‘S. Stoilow’ of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania email [email protected]
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Abstract

We provide a complete characterization of extreme points of the space of sofic representations. We also show that the restriction map $\text{Sof}(G,P^{{\it\omega}})$ to $\text{Sof}(H,P^{{\it\omega}})$, where $H\subset G$, is not always surjective. The first part of the paper is a continuation of Păunescu [A convex structure on sofic embeddings. Ergod. Th. & Dynam. Sys.34(4) (2014), 1343–1352] and follows more closely the plan of Brown [Topological dynamical systems associated to $\text{II}_{1}$-factors. Adv. Math.227(4) (2011), 1665–1699].

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 5 , August 2016 , pp. 1596 - 1615
Copyright
© Cambridge University Press, 2015 

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