scholarly journals Some unique group-measure space decomposition results

2013 ◽  
Vol 162 (11) ◽  
pp. 1923-1966 ◽  
Author(s):  
Ionut Chifan ◽  
Jesse Peterson
Keyword(s):  
Measure Space ◽  
Space Decomposition ◽  
Group Measure

scholarly journals II1 FACTORS AND EQUIVALENCE RELATIONS WITH DISTINCT FUNDAMENTAL GROUPS

2013 ◽  
Vol 24 (03) ◽  
pp. 1350016
Author(s):  
J. KEERSMAEKERS ◽  
A. SPEELMAN
Keyword(s):  
Fundamental Group ◽  
Equivalence Relation ◽  
Measure Space ◽  
Cartan Subalgebra ◽  
Equivalence Relations ◽  
Fundamental Groups ◽  
Cartan Subalgebras ◽  
Group Measure

We construct a group measure space II1 factor that has two nonconjugate Cartan subalgebras. We show that the fundamental group of the II1 factor is trivial, while the fundamental group of the equivalence relation associated with the second Cartan subalgebra is nontrivial. This is not absurd as the second Cartan inclusion is twisted by a 2-cocycle.

scholarly journals Inner amenability for groups and central sequences in factors

2014 ◽  
Vol 36 (4) ◽  
pp. 1106-1129 ◽  
Author(s):  
IONUT CHIFAN ◽  
THOMAS SINCLAIR ◽  
BOGDAN UDREA
Keyword(s):  
Measure Space ◽  
Negative Curvature ◽  
Mapping Class ◽  
Discrete Groups ◽  
Class Groups ◽  
Curvature Condition ◽  
Von Neumann ◽  
Group Measure ◽  
Central Sequences ◽  
Inner Amenability

We show that a large class of i.c.c., countable, discrete groups satisfying a weak negative curvature condition are not inner amenable. By recent work of Hull and Osin [Groups with hyperbolically embedded subgroups. Algebr. Geom. Topol.13 (2013), 2635–2665], our result recovers that mapping class groups and $\text{Out}(\mathbb{F}_{n})$ are not inner amenable. We also show that the group-measure space constructions associated to free, strongly ergodic p.m.p. actions of such groups do not have property Gamma of Murray and von Neumann [On rings of operators IV. Ann. of Math. (2) 44 (1943), 716–808].

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